Question

I’m not firmiliar with the sun or difference of cubes (HW assignment)

Answer 1

Given:

`125r^3-216`

Find-: Factor using the formula of the sum or difference of cube.

Sol:

Factoring sum and differences of cubs is:

`\begin{gathered} x^3-y^3=(x-y)(x^2+y^2+xy) \\ \\ x^3+y^3=(x+y)(x^2+y^2-xy) \end{gathered}`

Apply for the given information.

`\begin{gathered} =125r^3-216 \\ \\ =(5r)^3-(6)^3 \end{gathered}`
`\begin{gathered} x^3-y^3=(x-y)(x^2+y^2+xy) \\ \\ (5r)^3-(6)^3=(5r-6)((5r)^2+(6)^2+(5r)(6)) \\ \\ =(5r-6)(25r^2+36+30r) \end{gathered}`