Factorizing a Difficult Polynomial: Using the Difference of Squares Identity

[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?

 

[stringy]

Hello there.

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

 

[Heidegger]

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 going to try.

 

[Mark44]

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

I'm going to try.

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

 

[stringy]

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

 

[Heidegger]

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.