Question

How do you factor `(2c+3)^3 - (c-4)^3`?

Answer 1

Temporarily simplify by letting
`p = (2c+3)`
and
`q=(c-4)`

`(2c+3)^3 - (c-4)^3`
becomes
`p^3-q^3`
which factors as
`(p-q)(p^2+pq+q^2)`

Re-inserting the original values for `p` and `q`
`(2c+3-(c-4))*( (2c+3)^2 +(2c+3)(c-4) +(c-4)^2))`

`= (c+7) *((4c^2+12c+9) +(2c^2-5c-12)+(c^2-8c+16))`

`=(c+7)(7c^2-c+13)`
...assuming I've been able to keep all my terms straight