Prove the following identity: a3 – b3 = (a – b)(a² + ab + b²)

Q: PROVE: Z3 = 26 k 2 4 3 a 5 8 7 b LO

A: Given:

Q: 4x (3x - 1) %3D -12х + 4 О Tue O False

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Q: Show that B is the multiplicative inverse of A, where:

A: Two matrices, A and B are said to be multiplicative inverses of each other if AB and BA both results…

Q: 10 a.) Completely simplify E ()2* i=0 b.) Expand (1 – r)® and simplify. c.) Expand (r +r-1)5 and…

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Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: In AABC, DE || BC, find x. x+2 D. 6, E x+1 C 2.

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Q: Evaluate the followng- (メー2メ+3) dx ー2 Cos (70+5) dO

A: Formula used: 1)∫xn dx=xn+1n+1+C and 2) ∫cosx dx=sinx+C, where C is integrating constant. Given: 1)…

Q: Let a = - 4i – 33+ 3k and b = 4i – 33+ 2k. Find a – 36.

A: given   a→=-4i→-3j→+3k→    and  b→=4i→-3j→+2k→ we have to find a→-3b→

Q: Find the adjoint of the operation B = 2|0 × 1|- ; | 1 ×o |

A: This question asks to find the adjoint of the operation B^=2|0×1|-i|1×0|.

Q: evaluate (1 – 2i) – (-3+ 4i) O V13e-0.983i O 2V13e -0.983i A O 2 13e0.983i O 13/2e0.983i

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Q: 1 2 Perform the indicated operations when A = 0 -1 A(I + A) = =

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Q: √16 + √95 se 25

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Q: Determine how AABC was translated. ...

A: We can use the graphical translation in order to solve the given problem.

Q: Use the union rule to answer. If n(A) = 10, n(B) = 15 and n(AB) = 8, what is n(A U B)?

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Q: fnd the dorminof the function +4 ベ+!

A: Given:

Q: 16 + 25 25

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Q: O Determine rand s so that, 3.

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Q: 6) Find (cor dy of

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Q: Suppose Zı= 4+4i , Z2= 5 +7i. Evaluate (a) 2 Z1– 4 Z2 Z2 (b) 3 Z1

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Q: Evaluate: S O (1+2√√)¹ 2 O (1+2√)¹ +C 8 O 2(1+2√x) + C O (1+2√)¹ - + C 4 (1+2√x)³ - dx +C

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Q: Find a pair of integers x and y such that 66x + 48y = gcd(66, 48)

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Q: Determine Proy,b si ā = 3i– 4j+2k y b = -2i+3j-k

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Q: 3. State the GCF of each pair of terms. a) 6x and 10x b) 154³ and 20² c) ab and a²6² d) -2x¹y¹ and…

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Q: 2. If p = 41+2j – k, q = 6i+ 6j– 2k and 7 = -3i – 4j– 3k, evaluate a) q• (p- 2r) b) (r +g• p) c)…

A: Here we use formula of dot product of two vector, and addition, subtraction, multiplication of…

Q: b.) (-38/135 +65/70) (3 + 4i) 5 + 2i

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Q: A + B) E Mmxn - (B + C) = (A + B) + C +0= A

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Q: 27a³b?c Simplify: -3abc

A: Here we have to simplify the given expression. We have  27a3b2c-3abc Now we can write  27 = 3*3*3…

Q: Evaluate: - 2)(5 – 3r)"dr 10

A: the given integral is: ∫-11x-25-3x10 dx we have to evaluate the given integral.

Q: Find the following expressions if a = (6r, 0, r), b = (6s, –s, 7s), and c = (2t, 10t, 5). a ·b = 1.…

A: We need to find dot product.

Q: If a = 2i+3j -4k and b 7i-10j +9k find a b. a b ||(Simplify your answer.)

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Q: [5 A = Let -3 -4 1 C = B = and 2] simplify AB+AC

A: Use the property of Matrix addition and multiplication to get this.

Q: Let ā = 6i – 5j and b 4i + j. Find a :

A: Here I am attaching image so that you understand each and every step.

Q: В Calculate A and B so that + %D 1+x 1-

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