Question

How do you factor `64x^3 + 27y^3`?

Answer 1

`(4x + 3y)(16x^2 -12xy + 9y^2)`

Explanation:

This expression is a `color(blue)" sum 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 `64x^3 = (4x)^3" and " 27y^3 = (3y)^3`

For factorising purposes a = 4x and b = 3y

`rArr 64x^3+27y^3= (4x+3y)(16x^2-12xy+9y^2)`