Factoring Polynomials: Sum and Difference of Cubes Assignment

Factor 125x9 + 64. (5x3 - 4)(25x6 + 20x3 + 16) (5x3 - 4)(25x3 + 20x3 + 16) (5x3 + 4)(25x6 - 20x3 + 16) (5x3 + 4)(25x3 - 20x3 + 16)

C

What is 64x12 - 1,000 written as a difference of cubes? (4x)3 - 103 (8x)3 - 1003 (4x4)3 - 103 (8x4)3 - 1003

C

What is the factored form of x3 + 125? (x3 + 5)(x6 - 5x3 + 25) (x3 - 5)(x6 + 5x3 + 25) (x + 5)(x2 - 5x + 25) (x - 5)(x2 + 5x + 25)

C

What is cbrt 125x^12? 5x2 5x4 25x2 25x4

B

Which are sums of perfect cubes? Check all that apply. 8x6 + 27 x9 + 1 81x3 + 16x6 x6 + x3 27x9 + x12 9x3 + 27x9

A B D E

Which are perfect cubes? Check all that apply. 64 x16 8x3 27x4 81x6 125x9

A C F

What is 64x6 + 27 written as a sum of cubes? (4x)3 + 33 (4x2)3 + 33 (4x2)3 + 93 (4x3)3 + 33

B

What is the factorization of 1,000x6 - 27? (10x2 - 3)(100x2 + 30x2 + 9) (10x2 - 3)(100x4 + 30x2 + 9) (10x3 - 3)(100x2 + 30x3 + 9) (10x3 - 3)(100x6 + 30x3 + 9)

B

Factor 64 - x15. (4 - x3)(16 + 4x3 + x3) (4 - x3)(16 + 4x3 + x6) (4 - x5)(16 + 4x5 + x5) (4 - x5)(16 + 4x5 + x10)

D

How would the sum of cubes formula be used to factor x3y3 + 343? Explain the process. Do not write the factorization.

To factor, first identify the quantities that are being cubed. The first term is the cube of xy, and the constant is the cube of 7. Next, use the formula to write the factors. The first factor is the sum of xy and 7. The second factor has three terms: the square of xy, the negative of 7xy, and the square of 7.