Question

How do you factor `8x^3 - 1000`?

Answer 1

`8(x-5)(x^2+5x+25)`

Explanation:

The first step is to 'take out' common factor of 8

`rArr 8x^3-1000 = 8(x^3-125)`

now `x^3-125color(blue)" is a difference of cubes "`

and 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))|)))`

now `x^3=(x)^3" and " 125=(5)^3`

for factorising purposes: a = x and b = 5

`rArr x^3-125=(x-5)(x^2+5x+25)`

`rArr 8x^3-1000=8(x-5)(x^2+5x+25)`