Question

Which products result in a sum or difference of cubes? Check all that apply. (x – 4)(x2 + 4x – 16) (x – 1)(x2 – x + 1) (x – 1)(x2 + x + 1) (x + 1)( + x – 1) (x + 4)(x2 – 4x + 16) (x + 4)(x2 + 4x + 16)

Answer 1

$a^3+b^3=(a+b)(a^2-ab+b^2)\\\\a^3-b^3=(a-b)(a^2+ab+b^2)\\\\(x-4)(x^2+4x\underline{-16})\qquad \mathbb{NOT}\\\\(x-1)(x^2\underline{-x}+1)\qquad\mathbb{NOT}\\\\(x-1)(x^2+x+1)=(x-1)(x^2+(x)(1)+1^2)\qquad\mathbb{YES}\\\\(x+1)(x^2+x\underline{-1})\qquad\mathbb{NOT}\\\\(x+4)(x^2-4x+16)=(x+4)(x^2+(x)(4)+4^2)\qquad\mathbb{YES}\\\\(x+4)(x^2\underline{+4x}+4)\qquad\mathbb{NOT}$

Answer 2

Answer:

See below.

Step-by-step explanation:

There are 2 identities:

a^3 - b^3  = (a - b)(a ^2 + ab + b^2)

a^3 + b^3 = (a + b) ( a^2 - ab + b^2)

So:-

(x - 1)(x^2 + x + 1)  = x^3 - 1    is the difference of 2 cubes.

(x + 4)(x^2 - 4x + 16) = x^3 + 64 is the sum of 2 cubes.