# Difficult factorisation

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?

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Hello there.

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

Hello there.

What do you know about the factorization of a difference of squares?
Ok so the solution could easily be found by just applying the distributive law?

I'm gonna try.

Mark44
Mentor
Ok so the solution could easily be found by just applying the distributive law?

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

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

More specifically, use the fact that a2 - b2 = (a + b)(a - b). That's what stringy was getting at.
EDIT: Mark44 beat me to it. For future reference, the difference of squares refers to the identity that Mark44 wrote.
Thank you. I will return later with my answer.