Question

How do you factor `4x^3 + 32`?

Answer 1

`4(x+2)(x^2-2x+4)`

Explanation:

First step is to take out a `color(blue)"common factor"` of 4.

`rArr4x^3+32=4(x^3+8)........ (A)`

Now, `x^3+8 color(blue)" is a sum of cubes"` and in general is factorised as follows.

`color(red)(|bar(ul(color(white)(a/a)color(black)(a^3+b^3=(a+b)(a^2-ab+b^2))color(white)(a/a)|)))........ (B)`

now, `(x)^3=x^3" and " (2)^3=8rArra=x" and "b=2`

substitute these values for a and b into (B)

`rArrx^3+8=(x+2)(x^2-2x+4)`

substitute back into (A)

`rArr4x^3+32=4(x+2)(x^2-2x+4)`