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All Textbook Solutions for Intermediate Algebra
In the following exercises, subtract the polynomials. 45. (12s215s)(s9)In the following exercises, subtract the polynomials. 46. (10r220r)(r8)In the following exercises, subtract the polynomials. 47. Subtract (9x2+2) from (12x2x+6)In the following exercises, subtract the polynomials. 48. Subtract (5y2y+12) from (10y28y20)In the following exercises, subtract the polynomials. 49. Subtract (7w24w+2) from (8w2w+6)In the following exercises, subtract the polynomials. 50. Subtract (5x2x+12) from (9x26x20)In the following exercises, find the difference of the polynomials. 51. Find the difference of (w2+w42) and (w210w+24)In the following exercises, find the difference of the polynomials. 52. Find the difference of (z23z18) and (z2+5z20)In the following exercises, add the polynomials. 53. (7x22xy+6y2)+(3x25xy)In the following exercises, add the polynomials. 54. (5x24xy3y2)+(2x27xy)In the following exercises, add the polynomials. 55. (7m2+mn8n2)+(3m2+2mn)In the following exercises, add the polynomials. 56. (2r23rs2s2)+(5r23rs)In the following exercises, add or subtract the polynomials. 57. (a2b2)(a2+3ab4b2)In the following exercises, add or subtract the polynomials. 58. (m2+2n2)(m28mnn2)In the following exercises, add or subtract the polynomials. 59. (p33p2q)+(2pq2+4q3)(3p2q+pq2)In the following exercises, add or subtract the polynomials. 60. (a32a2b)+(ab2+b3)(3a2b+4ab2)In the following exercises, add or subtract the polynomials. 61. (x3x2y)(4xy2y3)+(3x2yxy2)In the following exercises, add or subtract the polynomials. 62. (x32x2y)(xy23y3)(x2y4xy2)In the following exercises, find the function values for each polynomial function. 63. For the function f(x)=8x23x+2 , find: (a) f(5) (b) f(2) (c) f(0)In the following exercises, find the function values for each polynomial function. 64. For the function f(x)=5x2x7 , find: (a) f(4) (b) f(1) (c) f(0)In the following exercises, find the function values for each polynomial function. 65. For the function g(x)=436x , find: (a) g(3) (b) g(0) (c) g(1)In the following exercises, find the function values for each polynomial function. 66. For the function g(x)=1636x2 , find: (a) g(1) (b) g(0) (c) g(2)In the following exercises, find the height for each polynomial function. 67. A painter drops a brush from a platform 75 feet high. The polynomial function h(t)=16t2+75 gives the height of the brush t seconds after it was dropped. Find the height after t=2 seconds.In the following exercises, find the height for each polynomial function. 68. A girl drops a ball off the cliff into the ocean. The polynomial h(t)=16t2+200 gives the height of a ball t seconds after it is dropped. Find the height after t=3 seconds.In the following exercises, find the height for each polynomial function. 69. A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial function R(p)=4p2+420p . Find the revenue received when p=60 dollars.In the following exercises, find the height for each polynomial function. 70. A manufacturer of the latest basketball shoes has found that the revenue received from selling the shoes at a cost of p dollars each is given by the polynomial R(p)=4p2+420p . Find the revenue received when p=90 dollars.In the following exercises, find the height for each polynomial function. 71. The polynomial C(x)=6x2+90x gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and height 6 feet. Find the cost of producing a box with x=4 feet.In the following exercises, find the height for each polynomial function. 72. The polynomial C(x)=6x2+90x gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and height 4 feet. Find the cost of producing a box with x=6 feet.In each example, find (a) (f+g)(x)(b) (f+g)(2)(c) (fg)(x)(d) (fg)(3). 73. f(x)=2x24x+1 and g(x)=5x2+8x+3In each example, find (a) (f+g)(x)(b) (f+g)(2)(c) (fg)(x)(d) (fg)(3). 74. f(x)=4x27x+3 and g(x)=4x2+2x1In each example, find (a) (f+g)(x)(b) (f+g)(2)(c) (fg)(x)(d) (fg)(3). 75. f(x)=3x3x22x+3 and g(x)=3x37xIn each example, find (a) (f+g)(x)(b) (f+g)(2)(c) (fg)(x)(d) (fg)(3). 76. f(x)=5x3x2+3x+4 and g(x)=8x31Using your own words, explain the difference between a monomial, a binomial, and a trinomial.Using your own words, explain the difference between a polynomial with five terms and a polynomial with a degree of 5.Ariana thinks the sum 6y2+5y4 is 11y6. What is wrong with her reasoning?Is every trinomial a second degree polynomial? If not, give an example.Simplify each expression: (a) b9b8 (b) 42x4x (c) 3p54p (d) x6x4x8Simplify each expression: (a) x12x4 (b) 1010x (c) 2z6z7 (d) b5b9b5 .Simplify each expression: (a) x15x10 (b) 61465 (c) x18x22 (d) 12151230 .Simplify each expression: (a) y43y37 (b) 1015107 (c) m7m15 (d) 98919 .Simplify each expression: (a) 110 (b) q0 .Simplify each expression: (a) 230 (b) r0 .Simplify each expression: (a)z3 (b) 107 (c) 1p8 (d)143 .Simplify each expression: (a) n2 (b) 104 (c) 1q7 (d) 124 .Simplify each expression: (a) (23)4 (b) (mn)2 .Simplify each expression: (a) (35)3 (b) (ab)4 .Simplify each expression: (a) z4z5 (b) (p6q2)(p9q1) (c) (3u5v7)(4u4v2) .Simplify each expression: (a) c8c7 (b) (r5s3)(r7s5) (c) (6c6d4)(5c2d1) .Simplify each expression: (a) (b7)5 (b) (54)3 (c) (a4)5(a7)4 .Simplify each expression: (a)(z6)9 (b) (37)7 (c) (q4)5(q3)3 .Simplify each expression: (a) (2wx)5 (b) (11pq3)0 (c) (2b3)4 (d) (8a4)2 .Simplify each expression: (a) (3y)3 (b) (8m2n3)0 (c) (4x4)2 (d) (2c4)3 .Simplify each expression: (a) (p10)4 (b) (mn)7 (c) (3a b 3 c 2)4 (d) (3 x 2 y 3)3 .Simplify each expression: (a) (2q)3 (b) (wx)4 (c) (x y 33 z 2)2 (d) (2 m 2 n 2)3 .Simplify each expression: (a) (c4d2)5(3cd5)4 (b) ( a 2)3( a 2)4( a 4)5 (c) (3x y 2 x 2 y 3)2(9x y 3 x 3 y 2)1 .Simplify each expression: (a) (a3b2)6(4ab3)4 (b) ( p 3)4( p 5)3( p 7)6 (c) (4 x 3 y 2 x 2 y 1)2(8x y 3 x 2y)1 .Write in scientific notation: (a) 96,000 (b) 0.0078.Write in scientific notation: (a) 48,300 (b) 0.0129.Convert to decimal form: (a) 1.3103 (b) 1.2104 .Convert to decimal form: (a) 9.5104 (b) 7.5102 .Multiply or divide as indicated. Write answers in decimal form: (a) (3105)(2108) (b) 81024102 .Multiply or divide as indicated. Write answers in decimal form: (a) (3102)(3101) (b) 81042101 .In the following exercises, simplify each expression using the properties for exponents. 81. (a) d3d6 (b) 45x49x (c) 2y4y3 (d) ww2w3In the following exercises, simplify each expression using the properties for exponents. 82. (a) x4x2 (b) 89x83 (c) 3z255z8 (d) yy3y5In the following exercises, simplify each expression using the properties for exponents. 83. (a) n19n12 (b) 3x36 (c) 7w58w (d) a4a3a9In the following exercises, simplify each expression using the properties for exponents. 84. (a) q27q15 (b) 5x54x (c) 9u417u53 (d) c5c11c2In the following exercises, simplify each expression using the properties for exponents. 85. mxm3In the following exercises, simplify each expression using the properties for exponents. 86. nyn2In the following exercises, simplify each expression using the properties for exponents. 87. yaybIn the following exercises, simplify each expression using the properties for exponents. 88. xpxqIn the following exercises, simplify each expression using the properties for exponents. 89. (a) x18x3 (b) 51253 (c) q18q36 (d) 102103In the following exercises, simplify each expression using the properties for exponents. 90. (a) y20y10 (b) 71672 (c) t10t40 (d) 8385In the following exercises, simplify each expression using the properties for exponents. 91. (a) p21p7 (b) 41644 (c) bb9 (d)446In the following exercises, simplify each expression using the properties for exponents. 92. (a) u24u3 (b) 91595 (c) xx7 (d) 10103In the following exercises, simplify each expression using the properties for exponents. 93. (a) 200 (b) b0In the following exercises, simplify each expression using the properties for exponents. 94. (a) 130 (b) k0In the following exercises, simplify each expression using the properties for exponents. 95. (a) 270 (b) (270)In the following exercises, simplify each expression using the properties for exponents. 96. (a) 150 (b) (150)In the following exercises, simplify each expression. 97. (a) a2 (b) 103 (c) 1c5 (d) 132In the following exercises, simplify each expression. 98. (a) b4 (b) 102 (c) 1c5 (d) 152In the following exercises, simplify each expression. 99. (a) r3 (b) 105 (c) 1q10 (d) 1103In the following exercises, simplify each expression. 100. (a) s8 (b) 102 (c) 1t9 (d) 1104In the following exercises, simplify each expression. 101. (a) (58)2 (b) (ba)2In the following exercises, simplify each expression. 102. (a) (310)2 (b) (2z)3In the following exercises, simplify each expression. 103. (a) (49)3 (b) (uv)5In the following exercises, simplify each expression. 104. (a) (72)3 (b) (3x)3In the following exercises, simplify each expression. 105. (a) (5)2 (b) 52 (c) (15)2 (d) (15)2In the following exercises, simplify each expression. 106. (a) 53 (b) (15)3 (c) (15)3 (d)(5)3In the following exercises, simplify each expression. 107. (a) 351 (b) (35)1In the following exercises, simplify each expression. 108. (a) 342 (b) (34)2In the following exercises, simplify each expression using the Product Property. 109. (a) b4b8 (b) (w4x5)(w2x4) (c) (6c3d9)(2c4d5)In the following exercises, simplify each expression using the Product Property. 110. (a) s3s7 (b) (m3n3)(m5n1) (c) (2j5k8)(7j2k3)In the following exercises, simplify each expression using the Product Property. 111. (a) a4a3 (b) (uv2)(u5v3) (c) (4r2s8)(9r4s3)In the following exercises, simplify each expression using the Product Property. 112. (a) y5y5 (b) (pq4)(p6q3) (c) (5m4n6)(8m5n3)In the following exercises, simplify each expression using the Product Property. 113. p5p2p4In the following exercises, simplify each expression using the Product Property. 114. x4x2x3In the following exercises, simplify each expression using the Power Property. 115. (a) (m4)2 (b) (103)6 (c) (x3)4In the following exercises, simplify each expression using the Power Property. 116. (a) (b2)7 (b) (38)2 (c) (k2)5In the following exercises, simplify each expression using the Power Property. 117. (a) (y3)x (b) (5x)y (c) (q6)8In the following exercises, simplify each expression using the Power Property. 118. (a) (x2)y (b) (7a)b (c) (a9)10In the following exercises, simplify each expression using the Product to a Power Property. 119. (a) (3xy)2 (b) (6a)0 (c) (5x2)2 (d) (4y3)2In the following exercises, simplify each expression using the Product to a Power Property. 120. (a) (4ab)2 (b) (5x)0 (c) (4y3)3 (d) (7y3)2In the following exercises, simplify each expression using the Product to a Power Property. 121. (a) (5ab)3 (b) (4pq)0 (c) (6x3)2 (d) (3y4)2In the following exercises, simplify each expression using the Product to a Power Property. 122. (a) (3xyz)4 (b) (7mn)0 (c) (3x3)2 (d) (2y5)2In the following exercises, simplify each expression using the Quotient to a Power Property. 123. (a) (p2)5 (b) (xy)6 (c) (2x y 2z)3 (d) (4 p 3 q 2)2In the following exercises, simplify each expression using the Quotient to a Power Property. 124. (a) (x3)4 (b) (ab)5 (c) (2x y 2z)3 (d) (4 p 3 q 2)2In the following exercises, simplify each expression using the Quotient to a Power Property. 125. (a) (a3b)4 (b) (54m)2 (c) (2x y 2z)3 (d) (4 p 3 q 2)2In the following exercises, simplify each expression using the Quotient to a Power Property. 126. (a) (x2y)3 (b) (103q)4 (c) (2x y 2z)3 (d) (4 p 3 q 2)2In the following exercises, simplify each expression by applying several properties. 127. (a) (5t2)3(3t)2 (b) ( t 2)5( t 4)2( t 3)7 (c) (2x y 2 x 3 y 2)2(12x y 3 x 3 y 1)1In the following exercises, simplify each expression by applying several properties. 128. (a) (10k4)3(5k6)2 (b) ( q 3)6( q 2)3( q 4)8In the following exercises, simplify each expression by applying several properties. 129. (a) (m2n)2(2mn5)4 (b) (2 p 2)4(3 p 4)2(6 p 3)2In the following exercises, simplify each expression by applying several properties. 130. (a) (3pq4)2(6p6q)2 (b) (2 k 3)2(6 k 2)4(9 k 4)2In the following exercises, simplify each expression. 131. (a) 7n1 (b) (7n)1 (c) (7n)1€In the following exercises, simplify each expression. 132. (a) 6r1 (b) (6r)1 (c) (6r)1In the following exercises, simplify each expression. 133. (a) (3p)2 (b) 3p2 (c) 3p2In the following exercises, simplify each expression. 134. (a) (2q)4 (b) 2q4 (c) 2q4In the following exercises, simplify each expression. 135. (x2)4(x3)2In the following exercises, simplify each expression. 136. (y4)3(y5)2In the following exercises, simplify each expression. 137. (a2)6(a3)8In the following exercises, simplify each expression. 138. (b7)5(b2)6In the following exercises, simplify each expression. 139. (2m6)3In the following exercises, simplify each expression. 140. (3y2)4In the following exercises, simplify each expression. 141. (10x2y)3In the following exercises, simplify each expression. 142. (2mn4)5In the following exercises, simplify each expression. 143. (2a3b2)4In the following exercises, simplify each expression. 144. (10u2v4)3In the following exercises, simplify each expression. 145. (23x2y)3In the following exercises, simplify each expression. 146. (79pq4)2In the following exercises, simplify each expression. 147. (8a3)2(2a)4In the following exercises, simplify each expression. 148. (5r2)3(3r)2In the following exercises, simplify each expression. 149. (10p4)3(5p6)2In the following exercises, simplify each expression. 150. (4x3)3(2x5)4In the following exercises, simplify each expression. 151. (12x2y3)4(4x5y3)2In the following exercises, simplify each expression. 152. (13m3n2)4(9m8n3)2In the following exercises, simplify each expression. 153. (3m2n)2(2mn5)4In the following exercises, simplify each expression. 154. (2pq4)3(5p6q)2In the following exercises, simplify each expression. 155. (a) (3x)2(5x) (b) (2y)3(6y)In the following exercises, simplify each expression. 156. (a) (12y2)3(23y)2 (b) (12j2)5(25j3)2In the following exercises, simplify each expression. 157. (a) (2r2)3(41r)2 (b) (3x3)3(31x5)4In the following exercises, simplify each expression. 158. ( k 2 k 8 k 3)2In the following exercises, simplify each expression. 159. ( j 2 j 5 j 4)3In the following exercises, simplify each expression. 160. (4 m 3)2(5 m 4)3(10 m 6)3In the following exercises, simplify each expression. 161. (10 n 2)3(4 n 5)2(2 n 8)2In the following exercises, write each number in scientific notation. 162. (a) 57,000 (b) 0.026In the following exercises, write each number in scientific notation. 163. (a) 340,000 (b) 0.041In the following exercises, write each number in scientific notation. 164. (a) 8,750,000 (b) 0.00000871In the following exercises, write each number in scientific notation. 165. (a) 1,290,000 (b) 0.00000103In the following exercises, convert each number to decimal form. 166. (a) 5.2102 (b) 2.5102In the following exercises, convert each number to decimal form. 167. (a) 8.3102 (b) 3.8102In the following exercises, convert each number to decimal form. 168. (a) 7.5106 (b) 4.13105In the following exercises, convert each number to decimal form. 169. (a) 1.61010 (b) 8.43106In the following exercises, multiply or divide as indicated. Write your answer in decimal form. 170. (a) (3105)(3109) (b) 71031107In the following exercises, multiply or divide as indicated. Write your answer in decimal form. 171. (a) (2102)(1104) (b) 510211010In the following exercises, multiply or divide as indicated. Write your answer in decimal form. 172. (a) (7.1102)(2.4104) (b) 61043102In the following exercises, multiply or divide as indicated. Write your answer in decimal form. 173. (a) (3.5104)(1.6102) (b) 81064101Use the Product Property for Exponents to explain why xx=x2 .Jennifer thinks the quotient a24a6 simplifies to a4 . What is wrong with her reasoning?Explain why 53=(5)3 but 54(5)4 .When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?Multiply: (a) (5y7)(7y4) (b) (25a4b3)(15ab3) .Multiply: (a) (6b4)(9b5) (b) (23r5s)(12r6s7) .Multiply: (a) 3y(5y2+8y7) (b) 4x2y2(3x25xy+3y2) .Multiply: (a) 4x2(2x23x+5) (b) 6a3b(3a22ab+6b2) .Multiply: (a) (x+8)(x+9) (b) (3c+4)(5c2) .Multiply: (a) (5x+9)(4x+3) (b) (5y+2)(6y3) .Multiply: (a) (x7)(x+5) (b) (3x+7)(5x2) .Multiply: (a) (b3)(b+6) (b) (4y+5)(4y10) .Multiply: (a) (x2+6)(x8) (b) (2ab+5)(4ab4) .Multiply: (a) (y2+7)(y9) (b) (2xy+3)(4xy5) .Multiply using the Vertical Method: (5m7)(3m6) .Multiply using the Vertical Method: (6b5)(7b3) .Multiply (y3)(y25y+2) using (a) the Distributive Property and (b) the Vertical Method.Multiply (x+4)(2x23x+5) using (a) the Distributive Property and (b) the Vertical Method.Multiply: (a) (x+9)2 (b) (2cd)2 .Multiply: (a) (y+11)2 (b) (4x5y)2 .Multiply: (a) (6x+5)(6x5) (b) (4p7q)(4p+7q) .Multiply: (a) (2x+7)(2x7) (b) (3xy)(3x+y) .Choose the appropriate pattern and use it to find the product: (a) (9b2)(2b+9) (b) (9p4)2 (c) (7y+1)2 (d) (4r3)(4r+3)Choose the appropriate pattern and use it to find the product: (a) (6x+7)2 (b) (3x4)(3x+4) (c) (2x5)(5x2) (d) (6n1)2For functions f(x)=x5 and g(x)=x22x+3 , find (a) (fg)(x) (b) (fg)(2) .For functions f(x7) and g(x)=x2+8x+4 , find (a) (fg)(x) (b) (fg)(2) .In the following exercises, multiply the monomials. 178. (a) (6y7)(3y4) (b) (47rs2)(14rs3)In the following exercises, multiply the monomials. 179. (a) (10x5)(3x3) (b) (58x3y)(24x5y)In the following exercises, multiply the monomials. 180. (a) (8u6)(9u) (b) (23x2y)(34xy2)In the following exercises, multiply the monomials. 181. (a) (6c4)(12c) (b) (35m3n2)(59m2n3)In the following exercises, multiply. 182. (a) 8x(x2+2x15) (b) 5pq3(p22pq+6q2)In the following exercises, multiply. 183. (a) 5t(t2+3t18); (b) 9r3s(r23rs+5s2)In the following exercises, multiply. 184. (a) 8y(y2+2y15) (b) 4y2z2(3y2+12yzz2)In the following exercises, multiply. 185. (a) 5m(m2+3m18) (b) 3x2y2(7x2+10xyy2)In the following exercises, multiply the binomials using (a) the Distributive Property; (b) the FOIL method; (c) the Vertical Method. 186. (w+5)(w+7)In the following exercises, multiply the binomials using (a) the Distributive Property; (b) the FOIL method; (c) the Vertical Method. 187. (y+9)(y+3)In the following exercises, multiply the binomials using (a) the Distributive Property; (b) the FOIL method; (c) the Vertical Method. 188. (4p+11)(5p4)In the following exercises, multiply the binomials using (a) the Distributive Property; (b) the FOIL method; (c) the Vertical Method. 189. (7q+4)(3q8)In the following exercises, multiply the binomials. Use any method. 190. (x+8)(x+3)In the following exercises, multiply the binomials. Use any method. 191. (y6)(y2)In the following exercises, multiply the binomials. Use any method. 192. (2t9)(10t+1)In the following exercises, multiply the binomials. Use any method. 193. (6p+5)(p+1)In the following exercises, multiply the binomials. Use any method. 194. (q5)(q+8)In the following exercises, multiply the binomials. Use any method. 195. (m+11)(m4)In the following exercises, multiply the binomials. Use any method. 196. (7m+1)(m3)In the following exercises, multiply the binomials. Use any method. 197. (3r8)(11r+1)In the following exercises, multiply the binomials. Use any method. 198. (x2+3)(x+2)In the following exercises, multiply the binomials. Use any method. 199. (y24)(y+3)In the following exercises, multiply the binomials. Use any method. 200. (5ab1)(2ab+3)In the following exercises, multiply the binomials. Use any method. 201. (2xy+3)(3xy+2)In the following exercises, multiply the binomials. Use any method. 202. (x2+8)(x25)In the following exercises, multiply the binomials. Use any method. 203. (y27)(y24)In the following exercises, multiply the binomials. Use any method. 204. (6pq3)(4pq5)In the following exercises, multiply the binomials. Use any method. 205. (3rs7)(3rs4)In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method. 206. (x+5)(x2+4x+3)In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method. 207. (u+4)(u2+3u+2)In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method. 208. (y+8)(4y2+y7)In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method. 209. (a+10)(3a2+a5)In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method. 210. (y23y+8)(4y2+y7)In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method. 211. (2a25a+10)(3a2+a5)In the following exercises, multiply. Use either method. 212. (w7)(w29w+10)In the following exercises, multiply. Use either method. 213. (p4)(p26p+9)In the following exercises, multiply. Use either method. 214. (3q+1)(q24q5)In the following exercises, multiply. Use either method. 215. (6r+1)(r27r9)In the following exercises, square each binomial using the Binomial Squares Pattern. 216. (w+4)2In the following exercises, square each binomial using the Binomial Squares Pattern. 217. (q+12)2In the following exercises, square each binomial using the Binomial Squares Pattern. 218. (3xy)2In the following exercises, square each binomial using the Binomial Squares Pattern. 219. (2y3z2)In the following exercises, square each binomial using the Binomial Squares Pattern. 220. (y+14)2In the following exercises, square each binomial using the Binomial Squares Pattern. 221. (x+23)2In the following exercises, square each binomial using the Binomial Squares Pattern. 222. (15x17y)2In the following exercises, square each binomial using the Binomial Squares Pattern. 223. (18x19y)2In the following exercises, square each binomial using the Binomial Squares Pattern. 224. (3x2+2)2In the following exercises, square each binomial using the Binomial Squares Pattern. 225. (5u2+9)2In the following exercises, square each binomial using the Binomial Squares Pattern. 226. (4y32)2In the following exercises, square each binomial using the Binomial Squares Pattern. 227. (8p33)2In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 228. (5k+6)(5k6)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 229. (8j+4)(8j4)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 230. (11k+4)(11k4)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 231. (9c+5)(9c5)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 232. (9c2d)(9c+2d)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 233. (7w+10x)(7w10x)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 234. (m+23n)(m23n)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 235. (p+45q)(p45q)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 236. (ab4)(ab+4)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 237. (xy9)(xy+9)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 238. (12p311q2)(12p3+11q2)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 239. (15m28n4)(15m2+8n4)In the following exercises, find each product. 240. (p3)(p+3)In the following exercises, find each product. 241. (t9)2In the following exercises, find each product. 242. (m+n)2In the following exercises, find each product. 243. (2x+y)(x2y)In the following exercises, find each product. 244. (2r+12)2In the following exercises, find each product. 245. (3p+8)(3p8)In the following exercises, find each product. 246. (7a+b)(a7b)In the following exercises, find each product. 247. (k6)2In the following exercises, find each product. 248. (a57b)2In the following exercises, find each product. 249. (x2+8y)(8xy2)In the following exercises, find each product. 250. (r6+s6)(r6s6)In the following exercises, find each product. 251. (y4+2z)2In the following exercises, find each product. 252. (x5+y5)(x5y5)In the following exercises, find each product. 253. (m38n)2In the following exercises, find each product. 254. (9p+8q)2In the following exercises, find each product. 255. (r2s3)(r3+s2)(10y6)+(4y7)(15p4)+(3p5)(x24x34)(x2+7x6)(j28j27)(j2+2j12)(15f8)(20f3)(14d5)(36d2)(4a3b)(9a2b6)(6m4n3)(7mn5)5m(m2+3m18)5q3(q22q+6)(s7)(s+9)(y22y)(y+1)(5xy)(x4)(6k1)(k2+2k4)(3x11y)(3x11y)(11b)(11+b)(rs27)(rs+27)(2x23y4)(2x2+3y4)(m15)2(3d+1)2(4a+10)2(3z+15)2For functions f(x)=x+2 and g(x)=3x22x+4 , find (a) (fg)(x) (b) (fg)(1)For functions f(x)=x1 and g(x)=4x2+3x5 , find (a) (fg)(x) (b) (fg)(2)For functions f(x)=2x7 and g(x)=2x+7 , find (a) (fg)(x) (b) (fg)(3)For functions f(x)=7x8 and g(x)=7x+8 , find (a) (fg)(x) (b) (fg)(2)For functions f(x)=x25x+2 and g(x)=x23x1 , find (a) (fg)(x) (b) (fg)(1)For functions f(x)=x2+4x3 and g(x)=x2+2x+4 , find (a) (fg)(x) (b) (fg)(1)Which method do you prefer to use when multiplying two binomials: the Distributive Property or the FOIL method? Why? Which method do you prefer to use when multiplying a polynomial by a polynomial: the Distributive Property or the Vertical Method? Why?Multiply the following: (x+2)(x2)(y+7)(y7)(w+5)(w5) Explain the pattern that you see in your answers.Multiply the following: (p+3)(p+3)(q+6)(q+6)(r+1)(r+1) Explain the pattern that you see in your answers.Why does (a+b)2 result in a trinomial, but (ab)(a+b) result in a binomial?Find the quotient: 72a7b3(8a12b4) .Find the quotient: 63c8d3(7c12d2) .Find the quotient: 28x5y1449x9y12 .Find the quotient: 30m5n1148m10n14 .Find the quotient: (32a2b16ab2)(8ab) .Find the quotient: (48a8b436a6b5)(6a3b3) .Find the quotient: (y2+10y+21)(y+3) .Find the quotient: (m2+9m+20)(m+4) .Find the quotient: (x47x2+7x+6)(x+3) .