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

Question

1672 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-11T20:22:35

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

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