Question

How do you factor (p+q)^3-(p-q)^3?

Please explain, don't just give the answer.

Answer 1

First, do you know how to factor in general the expression:

a^3 - b^3
?

Answer 2

(a-b) (a^2+a b+b^2)

Answer 3

Correct. Now set a = p + q and b = ....
and apply your formula.

Answer 4

Does b equal p-q? It got cut off

Answer 5

I didn't say, on purpose. But that would seem to make sense, wouldn't it?

Answer 6

Ah I see.

Answer 7

Happy factoring!

Answer 8

Just make sure you check your signs as you go.

Answer 9

I got 2 (3 p^2 q+q^3)

Answer 10

Looks good to me, as there are lots of cancelations.

Answer 11

Thanks again.

Answer 12

if we just calculated it out

(p+q)^3 - (p-q)^3
= p^3 + 3p^2q + 3pq^2 + q^3
-p^3 + 3p^2q - 3pq^2 + q^3
= 0 + 6p^2q + 0 + 2q^3
= 2(3p^2q + q^3)

Answer 13

So, likes lots of this in mathematics, there's more than one way to skin a cat.

Anyway -- got to move on! Cheers.