# Difficult factorisation

1. Aug 9, 2011

### Heidegger

The problem

Factorize: $a^{2}-\left ( b+c \right )^{2}$

expanded it to see if I can find any solution:

$\left ( b+c \right )^{2}=b^{2}+2bc+c^{2}$

$a^{2}-\left ( b^{2}+2bc+c^{2} \right )$

$a^{2}- b^{2}-2bc-c^{2} \right )$

But I can’t get any further.
What should I do now to simplify it? Please explain and show me a couple of clues or something?

2. Aug 9, 2011

### stringy

Hello there.

What do you know about the factorization of a difference of squares?

3. Aug 9, 2011

### Heidegger

Ok so the solution could easily be found by just applying the distributive law?

I'm gonna try.

4. Aug 9, 2011

### Staff: Mentor

More specifically, use the fact that a2 - b2 = (a + b)(a - b). That's what stringy was getting at.

5. Aug 9, 2011

### stringy

EDIT: Mark44 beat me to it. For future reference, the difference of squares refers to the identity that Mark44 wrote.

6. Aug 9, 2011

### Heidegger

Thank you. I will return later with my answer.