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