Question

How do you factor `27r^3 + 125s^3`?

Answer 1

`3r+5s)(9r^2-15rs+25s^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)`

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

`125s^3=(5s)^3rArrb=5s`

`rArr27r^3+125s^3`

`=(3r+5s)((3r)^2-(3rxx5s)+(5s)^2)`

`=(3r+5s)(9r^2-15rs+25s^2)`

Answer 2

`(3r+5s)*(9r^2-15rs+25s^2)`

Explanation:

show below

`27r^3 + 125s^3`

`(3r)^3+(5s)^3`

`(3r+5s)*(9r^2-15rs+25s^2)`

Note that

`x^3+y^3`

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