Question

How do you factor `27x^3+8y^3`?

Answer 1

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

Explanation:

`27x^3+8y^3`

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

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

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

Answer 2

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

Explanation:

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

Answer 3

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

Explanation:

`"this is a "color(blue)"sum of cubes"`

`"which factors in general as"`

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

`27x^3=(3x)^3rArra=3x`

`8y^3=(2y)^3rArrb=2y`

`rArr27x^3+8y^3=(3x+2y)((3x)^2-(3x xx2y)+(2y)^2)`

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