Question

8) Factor each sum or difference of cubes completely.
a. 8x3 + 27

Answer 1

`\large\boxed{(2x+3)(4x^2-6x+9)}`

Explanation:

`8=2^3\\\\8x^3=2^3x^3=(2x)^3\\\\27=3^3\\\\8x^3+27=(2x)^3+3^3\qquad\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+3)\bigg((2x)^2-(2x)(3)+3^2\bigg)=(2x+3)(4x^2-6x+9)`