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Math Algebra BEGINNING AND INTERMEDIATE AGEBRA

For Exercises 8–13, rewrite each binomial of the form ( a − b ) n as [ a + ( − b ) ] n . Then expand the binomials. Use Pascal’s triangle to find the coefficients. ( a − b 2 ) 4

For Exercises 8–13, rewrite each binomial of the form ( a − b ) n as [ a + ( − b ) ] n . Then expand the binomials. Use Pascal’s triangle to find the coefficients. ( a − b 2 ) 4

Solution Summary: The author calculates the expanded form of the binomial (a-b2)4 using the Pascal's triangle for the coefficients.

BEGINNING AND INTERMEDIATE AGEBRA

BEGINNING AND INTERMEDIATE AGEBRA

5th Edition

ISBN: 9781264367702

Author: Miller

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 14.1, Problem 12PE

For Exercises 8–13, rewrite each binomial of the form ( a − b ) n as [ a + ( − b ) ] n . Then expand the binomials. Use Pascal’s triangle to find the coefficients.

( a − b 2 ) 4

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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Chapter 14.1, Problem 11PE

Chapter 14.1, Problem 13PE

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Chapter 14 Solutions

BEGINNING AND INTERMEDIATE AGEBRA

Ch. 14.1 - Prob. 1SP Ch. 14.1 - Prob. 2SP Ch. 14.1 - Evaluate the expressions. 3. 1! Ch. 14.1 - Prob. 4SP Ch. 14.1 - Prob. 5SP Ch. 14.1 - Prob. 6SP Ch. 14.1 - Write out the first three terms of ( x + y ) 5 .Ch. 14.1 - 8. Use the binomial theorem to expand . Ch. 14.1 - Use the binomial theorem to expand ( 2 a − 3 b 2 )...Ch. 14.1 - Find the fourth term of ( x + y ) 8 .

Ch. 14.1 - 11. Find the fifth term of . Ch. 14.1 - a. The expanded form of ( x + b ) 2 =...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For a > 0 and b > 0 , what happens to the signs of...Ch. 14.1 - For Exercises 15–18, evaluate the expression. (See...Ch. 14.1 - For Exercises 15–18, evaluate the expression. (See...Ch. 14.1 - For Exercises 15–18, evaluate the expression. (See...Ch. 14.1 - For Exercises 15–18, evaluate the expression. (See...Ch. 14.1 - True or false: 0 ! ≠ 1 !Ch. 14.1 - True or false: n! is defined for negative...Ch. 14.1 - True or false: n ! = n for n = 1 and 2 .Ch. 14.1 - 22. Show that ! Ch. 14.1 - Show that 6 ! = 6 ⋅ 5 !Ch. 14.1 - Show that 8 ! = 8 ⋅ 7 !Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - Prob. 33PE Ch. 14.1 - Prob. 34PE Ch. 14.1 - Prob. 35PE Ch. 14.1 - For Exercises 33–36, find the first three terms of...Ch. 14.1 - Prob. 37PE Ch. 14.1 - Prob. 38PE Ch. 14.1 - Prob. 39PE Ch. 14.1 - Prob. 40PE Ch. 14.1 - For Exercises 39–50, use the binomial theorem to...Ch. 14.1 - Prob. 42PE Ch. 14.1 - Prob. 43PE Ch. 14.1 - Prob. 44PE Ch. 14.1 - Prob. 45PE Ch. 14.1 - For Exercises 39–50, use the binomial theorem to...Ch. 14.1 - Prob. 47PE Ch. 14.1 - For Exercises 39–50, use the binomial theorem to...Ch. 14.1 - Prob. 49PE Ch. 14.1 - Prob. 50PE Ch. 14.1 - Prob. 51PE Ch. 14.1 - Prob. 52PE Ch. 14.1 - Prob. 53PE Ch. 14.1 - Prob. 54PE Ch. 14.1 - Prob. 55PE Ch. 14.1 - For Exercises 51–56, find the indicated term of...Ch. 14.2 - Prob. 1SP Ch. 14.2 - Prob. 2SP Ch. 14.2 - Prob. 3SP Ch. 14.2 - Prob. 4SP Ch. 14.2 - Prob. 5SP Ch. 14.2 - Prob. 6SP Ch. 14.2 - Prob. 7SP Ch. 14.2 - Prob. 8SP Ch. 14.2 - Prob. 9SP Ch. 14.2 - Prob. 10SP Ch. 14.2 - Prob. 11SP Ch. 14.2 - Prob. 12SP Ch. 14.2 - Prob. 1PE Ch. 14.2 - Prob. 2PE Ch. 14.2 - Prob. 3PE Ch. 14.2 - Prob. 4PE Ch. 14.2 - Prob. 5PE Ch. 14.2 - Prob. 6PE Ch. 14.2 - Prob. 7PE Ch. 14.2 - Prob. 8PE Ch. 14.2 - Prob. 9PE Ch. 14.2 - Prob. 10PE Ch. 14.2 - Prob. 11PE Ch. 14.2 - Prob. 12PE Ch. 14.2 - Prob. 13PE Ch. 14.2 - Prob. 14PE Ch. 14.2 - Prob. 15PE Ch. 14.2 - Prob. 16PE Ch. 14.2 - Prob. 17PE Ch. 14.2 - Prob. 18PE Ch. 14.2 - Prob. 19PE Ch. 14.2 - Prob. 20PE Ch. 14.2 - Prob. 21PE Ch. 14.2 - Prob. 22PE Ch. 14.2 - Prob. 23PE Ch. 14.2 - Prob. 24PE Ch. 14.2 - Prob. 25PE Ch. 14.2 - Prob. 26PE Ch. 14.2 - Prob. 27PE Ch. 14.2 - Prob. 28PE Ch. 14.2 - Prob. 29PE Ch. 14.2 - For Exercises 21–32, find a formula for the nth...Ch. 14.2 - Prob. 31PE Ch. 14.2 - Prob. 32PE Ch. 14.2 - Edmond borrowed $500. To pay off the loan, he...Ch. 14.2 - Prob. 34PE Ch. 14.2 - Prob. 35PE Ch. 14.2 - Prob. 36PE Ch. 14.2 - Prob. 37PE Ch. 14.2 - Prob. 38PE Ch. 14.2 - Prob. 39PE Ch. 14.2 - Prob. 40PE Ch. 14.2 - Prob. 41PE Ch. 14.2 - Prob. 42PE Ch. 14.2 - Prob. 43PE Ch. 14.2 - Prob. 44PE Ch. 14.2 - Prob. 45PE Ch. 14.2 - Prob. 46PE Ch. 14.2 - For Exercises 39–54, find the sums. (See Examples...Ch. 14.2 - Prob. 48PE Ch. 14.2 - For Exercises 39–54, find the sums. (See Examples...Ch. 14.2 - Prob. 50PE Ch. 14.2 - Prob. 51PE Ch. 14.2 - Prob. 52PE Ch. 14.2 - Prob. 53PE Ch. 14.2 - For Exercises 39–54, find the sums. (See Examples...Ch. 14.2 - Prob. 55PE Ch. 14.2 - Prob. 56PE Ch. 14.2 - Prob. 57PE Ch. 14.2 - Prob. 58PE Ch. 14.2 - Prob. 59PE Ch. 14.2 - Prob. 60PE Ch. 14.2 - Prob. 61PE Ch. 14.2 - Prob. 62PE Ch. 14.2 - Prob. 63PE Ch. 14.2 - For Exercises 55–66, write the series in summation...Ch. 14.2 - Prob. 65PE Ch. 14.2 - Prob. 66PE Ch. 14.2 - Prob. 67PE Ch. 14.2 - Prob. 68PE Ch. 14.2 - Prob. 69PE Ch. 14.2 - Prob. 70PE Ch. 14.2 - 71. A famous sequence in mathematics is called the...Ch. 14.3 - Prob. 1SP Ch. 14.3 - Prob. 2SP Ch. 14.3 - Prob. 3SP Ch. 14.3 - Prob. 4SP Ch. 14.3 - Prob. 5SP Ch. 14.3 - Prob. 1PE Ch. 14.3 - Prob. 2PE Ch. 14.3 - Prob. 3PE Ch. 14.3 - Prob. 4PE Ch. 14.3 - Prob. 5PE Ch. 14.3 - Prob. 6PE Ch. 14.3 - Prob. 7PE Ch. 14.3 - Prob. 8PE Ch. 14.3 - Prob. 9PE Ch. 14.3 - For Exercises 7–12, the first term of an...Ch. 14.3 - Prob. 11PE Ch. 14.3 - Prob. 12PE Ch. 14.3 - Prob. 13PE Ch. 14.3 - Prob. 14PE Ch. 14.3 - Prob. 15PE Ch. 14.3 - Prob. 16PE Ch. 14.3 - Prob. 17PE Ch. 14.3 - Prob. 18PE Ch. 14.3 - Prob. 19PE Ch. 14.3 - Prob. 20PE Ch. 14.3 - Prob. 21PE Ch. 14.3 - Prob. 22PE Ch. 14.3 - Prob. 23PE Ch. 14.3 - Prob. 24PE Ch. 14.3 - Prob. 25PE Ch. 14.3 - Prob. 26PE Ch. 14.3 - Prob. 27PE Ch. 14.3 - Prob. 28PE Ch. 14.3 - Prob. 29PE Ch. 14.3 - For Exercises 25–33, write the nth term of the...Ch. 14.3 - For Exercises 25–33, write the nth term of the...Ch. 14.3 - Prob. 32PE Ch. 14.3 - Prob. 33PE Ch. 14.3 - Prob. 34PE Ch. 14.3 - Prob. 35PE Ch. 14.3 - Prob. 36PE Ch. 14.3 - Prob. 37PE Ch. 14.3 - Prob. 38PE Ch. 14.3 - Prob. 39PE Ch. 14.3 - Prob. 40PE Ch. 14.3 - Prob. 41PE Ch. 14.3 - Prob. 42PE Ch. 14.3 - Prob. 43PE Ch. 14.3 - For Exercises 42–49, find the number of terms, n,...Ch. 14.3 - Prob. 45PE Ch. 14.3 - Prob. 46PE Ch. 14.3 - Prob. 47PE Ch. 14.3 - Prob. 48PE Ch. 14.3 - Prob. 49PE Ch. 14.3 - Prob. 50PE Ch. 14.3 - Prob. 51PE Ch. 14.3 - Prob. 52PE Ch. 14.3 - Prob. 53PE Ch. 14.3 - Prob. 54PE Ch. 14.3 - For Exercises 53–66, find the sum of the...Ch. 14.3 - Prob. 56PE Ch. 14.3 - Prob. 57PE Ch. 14.3 - Prob. 58PE Ch. 14.3 - For Exercises 53–66, find the sum of the...Ch. 14.3 - Prob. 60PE Ch. 14.3 - Prob. 61PE Ch. 14.3 - Prob. 62PE Ch. 14.3 - Prob. 63PE Ch. 14.3 - Prob. 64PE Ch. 14.3 - For Exercises 53–66, find the sum of the...Ch. 14.3 - Prob. 66PE Ch. 14.3 - Find the sum of the first 100 positive integers.Ch. 14.3 - Prob. 68PE Ch. 14.3 - Prob. 69PE Ch. 14.3 - A triangular array of dominoes has one domino in...Ch. 14.4 - Prob. 1SP Ch. 14.4 - Prob. 2SP Ch. 14.4 - Prob. 3SP Ch. 14.4 - Prob. 4SP Ch. 14.4 - Prob. 5SP Ch. 14.4 - Prob. 6SP Ch. 14.4 - Prob. 7SP Ch. 14.4 - Prob. 8SP Ch. 14.4 - 1. a. A ______________sequence is a sequence in...Ch. 14.4 - Prob. 2PE Ch. 14.4 - Prob. 3PE Ch. 14.4 - Prob. 4PE Ch. 14.4 - Prob. 5PE Ch. 14.4 - Prob. 6PE Ch. 14.4 - Prob. 7PE Ch. 14.4 - Prob. 8PE Ch. 14.4 - Prob. 9PE Ch. 14.4 - Prob. 10PE Ch. 14.4 - Prob. 11PE Ch. 14.4 - Prob. 12PE Ch. 14.4 - Prob. 13PE Ch. 14.4 - Prob. 14PE Ch. 14.4 - Prob. 15PE Ch. 14.4 - Prob. 16PE Ch. 14.4 - Prob. 17PE Ch. 14.4 - Prob. 18PE Ch. 14.4 - Prob. 19PE Ch. 14.4 - Prob. 20PE Ch. 14.4 - For Exercises 19–24, write the first five terms of...Ch. 14.4 - Prob. 22PE Ch. 14.4 - Prob. 23PE Ch. 14.4 - For Exercises 19–24, write the first five terms of...Ch. 14.4 - Prob. 25PE Ch. 14.4 - Prob. 26PE Ch. 14.4 - Prob. 27PE Ch. 14.4 - Prob. 28PE Ch. 14.4 - For Exercises 25–30, find the n th term of each...Ch. 14.4 - Prob. 30PE Ch. 14.4 - Prob. 31PE Ch. 14.4 - Prob. 32PE Ch. 14.4 - Prob. 33PE Ch. 14.4 - Prob. 34PE Ch. 14.4 - Prob. 35PE Ch. 14.4 - Prob. 36PE Ch. 14.4 - Prob. 37PE Ch. 14.4 - Prob. 38PE Ch. 14.4 - Prob. 39PE Ch. 14.4 - Prob. 40PE Ch. 14.4 - Prob. 41PE Ch. 14.4 - If the second and third terms of a geometric...Ch. 14.4 - 43. Explain the difference between a geometric...Ch. 14.4 - Prob. 44PE Ch. 14.4 - Prob. 45PE Ch. 14.4 - Prob. 46PE Ch. 14.4 - Prob. 47PE Ch. 14.4 - Prob. 48PE Ch. 14.4 - Prob. 49PE Ch. 14.4 - Prob. 50PE Ch. 14.4 - Prob. 51PE Ch. 14.4 - Prob. 52PE Ch. 14.4 - For Exercises 47–56, find the sum of the geometric...Ch. 14.4 - For Exercises 47–56, find the sum of the geometric...Ch. 14.4 - For Exercises 47–56, find the sum of the geometric...Ch. 14.4 - For Exercises 47–56, find the sum of the geometric...Ch. 14.4 - Prob. 57PE Ch. 14.4 - Prob. 58PE Ch. 14.4 - Prob. 59PE Ch. 14.4 - Prob. 60PE Ch. 14.4 - Prob. 61PE Ch. 14.4 - Prob. 62PE Ch. 14.4 - Prob. 63PE Ch. 14.4 - Prob. 64PE Ch. 14.4 - Prob. 65PE Ch. 14.4 - Prob. 66PE Ch. 14.4 - Prob. 67PE Ch. 14.4 - Prob. 68PE Ch. 14.4 - Prob. 69PE Ch. 14.4 - Prob. 70PE Ch. 14.4 - Prob. 71PE Ch. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14.4 - Prob. 2PRE Ch. 14.4 - Prob. 3PRE Ch. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14.4 - Prob. 5PRE Ch. 14.4 - Prob. 6PRE Ch. 14.4 - Prob. 7PRE Ch. 14.4 - Prob. 8PRE Ch. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14.4 - Prob. 10PRE Ch. 14.4 - Prob. 11PRE Ch. 14.4 - Prob. 12PRE Ch. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14.4 - Prob. 14PRE Ch. 14.4 - Prob. 15PRE Ch. 14.4 - Prob. 16PRE Ch. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14 - Prob. 1RE Ch. 14 - Prob. 2RE Ch. 14 - Prob. 3RE Ch. 14 - Prob. 4RE Ch. 14 - Prob. 5RE Ch. 14 - Prob. 6RE Ch. 14 - Prob. 7RE Ch. 14 - Prob. 8RE Ch. 14 - Prob. 9RE Ch. 14 - 10. Find the middle term of the binomial...Ch. 14 - For Exercises 11–14, write the terms of the...Ch. 14 - Prob. 12RE Ch. 14 - Prob. 13RE Ch. 14 - Prob. 14RE Ch. 14 - Prob. 15RE Ch. 14 - Prob. 16RE Ch. 14 - Prob. 17RE Ch. 14 - Prob. 18RE Ch. 14 - For Exercises 19–20, find the sum of the...Ch. 14 - Prob. 20RE Ch. 14 - Prob. 21RE Ch. 14 - Prob. 22RE Ch. 14 - Prob. 23RE Ch. 14 - Prob. 24RE Ch. 14 - Prob. 25RE Ch. 14 - Prob. 26RE Ch. 14 - Prob. 27RE Ch. 14 - Prob. 28RE Ch. 14 - For Exercises 29–30, find the number of terms. 3 ,...Ch. 14 - Prob. 30RE Ch. 14 - Prob. 31RE Ch. 14 - Prob. 32RE Ch. 14 - For Exercises 33–36, find the sum of the...Ch. 14 - Prob. 34RE Ch. 14 - Prob. 35RE Ch. 14 - Prob. 36RE Ch. 14 - For Exercises 37–38, find the common ratio. 5 , 15...Ch. 14 - Prob. 38RE Ch. 14 - Prob. 39RE Ch. 14 - Prob. 40RE Ch. 14 - Prob. 41RE Ch. 14 - Prob. 42RE Ch. 14 - Prob. 43RE Ch. 14 - Prob. 44RE Ch. 14 - Prob. 45RE Ch. 14 - Prob. 46RE Ch. 14 - Prob. 47RE Ch. 14 - Prob. 48RE Ch. 14 - Prob. 49RE Ch. 14 - Prob. 50RE Ch. 14 - Prob. 51RE Ch. 14 - Prob. 1T Ch. 14 - Prob. 2T Ch. 14 - Prob. 3T Ch. 14 - Prob. 4T Ch. 14 - Find the sixth term. ( a − c 3 ) 8 Ch. 14 - Write the terms of the sequence. a n = − 3 n + 2 ;...Ch. 14 - 7. Find the sum. Ch. 14 - a. An 8-in. tomato seedling is planted on Sunday....Ch. 14 - Prob. 9T Ch. 14 - Find the common difference. 3 , 13 4 , 7 2 , ...Ch. 14 - 11. Find the common ratio. Ch. 14 - Prob. 12T Ch. 14 - Prob. 13T Ch. 14 - Prob. 14T Ch. 14 - Write an expression for the n th term of the...Ch. 14 - 16. Find the number of terms in the sequence. Ch. 14 - 17. Find the number of terms in the sequence. Ch. 14 - Prob. 18T Ch. 14 - 19. Find the sum of the geometric series. Ch. 14 - Prob. 20T Ch. 14 - Given a geometric series with a 6 = 9 and r = 3 ,...Ch. 14 - 22. Find the 18th term of the arithmetic sequence...Ch. 14 - Prob. 23T Ch. 14 - Prob. 1CRE Ch. 14 - Prob. 2CRE Ch. 14 - Prob. 3CRE Ch. 14 - Prob. 4CRE Ch. 14 - Prob. 5CRE Ch. 14 - Prob. 6CRE Ch. 14 - Prob. 7CRE Ch. 14 - Prob. 8CRE Ch. 14 - Prob. 9CRE Ch. 14 - Prob. 10CRE Ch. 14 - Prob. 11CRE Ch. 14 - Prob. 12CRE Ch. 14 - Prob. 13CRE Ch. 14 - For Exercises 14–17, factor completely. 6 a 2 − 17...Ch. 14 - Prob. 15CRE Ch. 14 - Prob. 16CRE Ch. 14 - For Exercises 14–17, factor completely. w 3 + 9 w...Ch. 14 - Prob. 18CRE Ch. 14 - Prob. 19CRE Ch. 14 - Prob. 20CRE Ch. 14 - For Exercises 18–25, solve the equation. ( 5 y − 2...Ch. 14 - Prob. 22CRE Ch. 14 - Prob. 23CRE Ch. 14 - Prob. 24CRE Ch. 14 - Prob. 25CRE Ch. 14 - 26. Write the expression as a single logarithm. Ch. 14 - 27. Use a calculator to approximate the value of...Ch. 14 - For Exercises 28–32, solve the inequality. Write...Ch. 14 - For Exercises 28–32, solve the inequality. Write...Ch. 14 - Prob. 30CRE Ch. 14 - For Exercises 28–32, solve the inequality. Write...Ch. 14 - Prob. 32CRE Ch. 14 - Prob. 33CRE Ch. 14 - Prob. 34CRE Ch. 14 - For Exercises 33–35, graph the equation. 35. Ch. 14 - Graph the solution set. x 2 9 + y 2 25 ≤ 1 Ch. 14 - 37. Given a. Determine the...Ch. 14 - Prob. 38CRE Ch. 14 - Write an equation of the line passing through the...Ch. 14 - Prob. 40CRE Ch. 14 - Prob. 41CRE Ch. 14 - Prob. 42CRE Ch. 14 - Prob. 43CRE Ch. 14 - Given the points ( 9 , − 4 ) and ( 3 , 0 ) , a....Ch. 14 - Prob. 45CRE Ch. 14 - The time t ( n ) (in minutes) required for a rat...Ch. 14 - The speed of a car varies inversely as the time to...Ch. 14 - Prob. 48CRE Ch. 14 - Prob. 49CRE Ch. 14 - 50. Against the wind, a plane can travel 4950 mi...

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