Question

How do you factor: `y= 8x^3 - 27`?

Answer 1

`(2x-3)(4x^2+6x+9)`

Explanation:

This expression is a`color(blue)" 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))color(white)(a/a)|)))`

now `8x^3=(2x)^3" and " 27=(3)^3`

For factorising purposes `a = 2x and b = 3`

`rArr 8x^3-27=(2x-3)(4x^2+6x+9)`