Question

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

Answer 1

`(x-2y)(x^2+2xy+4y^2)`

Explanation:

`x^3-8y^3`
`rArr (x)^3-(2y)^3`
`rArr(x-2y)^3+3.x.2y(x-2y)`
`rArr(x-2y)[(x-2y)^2+6xy]`
`rArr(x-2y)[x^2-4xy+4y^2+6xy]`
`rArr(x-2y)(x^2+2xy+4y^2)`

Answer 2

`(x-2y)(x^2+2xy+4y^2)`

Explanation:

`x^3-8y^3larrcolor(blue)"is a difference of cubes"`

`•color(white)(x)a^3-b^3=(a-b)(a^2+ab+b^2)`

`"here "a=x" and "b=2yto(2y)^3=8y^3`

`rArrx^3-8y^3=(x-2y)(x^2+2xy+4y^2)`

Answer 3

`x^3-8y^3=color(blue)((x-2y)(x^2+2xy+4y^2)`

Explanation:

Factor:

`x^3-8y^3`

Apply the difference of cubes:

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

where:

`a=x`, and `b=2y`

Plug in the known values.

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

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

Apply multiplicative distributive property: `(ab)^m=a^mb^m`

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

Simplify.

`(x-2y)(x^2+2xy+4y^2)`