Question

How do you factor `m^3 + (m+3)^3`?

Answer 1

`(2m+3)*(m^2+3m+9)`

Explanation:

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

Answer 2

`(2m+3)(m^2+3m+9)`

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)`

`"here "a=m" and "b=m+3`

`rArrm^3+(m+3)^3`

`=(m+m+3)(m^2-m(m+3)+(m+3)^2)`

`=(2m+3)(m^2-m^2-3m+m^2+6m+9)`

`=(2m+3)(m^2+3m+9)`