Question

Can you show me the steps to factor out 8x^3 - 27y^3?

Answer 1

`(2x-3y)(4x^2+6xy+9y^2)` is the factored form of
`8x^3-27y^3`

Solution:

We have to factor the given expression

`8x^3-27y^3`

We can use the algebraic identity to factor the given expression

`a^3-b^3=(a-b)(a^2+ab+b^2)`

Lets make the given expression in form of
`a^3-b^3`

`8x^3-27y^3=(2)^3(x)^3-(3)^3(y)^3`

`8x^3-27y^3=(2x)^3-(3y)^3`

Now apply the algebraic property in above expression

Here, a = 2x and b = 3y

Therefore,

`(2x)^3-(3y)^3=(2x-3y)((2x)^2+(2x)(3y)+(3y)^2)`

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

Thus the given expression is factored out