# Math Help - Factorisation

1. ## Factorisation

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

I’ve 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. ## Re: Factorisation

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

I’ve 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?
Answer: $(a-(b+c))(a+(b+c))$

3. ## Re: Factorisation

Originally Posted by Benjy
Factorize: $a^{2}-\left ( b+c \right )^{2}$
$a^{2}-\left ( b+c \right )^{2}=[a-(b+c)][a+(b+c)]$

4. ## Re: Factorisation

Originally Posted by Also sprach Zarathustra
Answer: $(a-(b+c))(a+(b+c))$

Originally Posted by Plato
$a^{2}-\left ( b+c \right )^{2}=[a-(b+c)][a+(b+c)]$
Thanks! Could you please explain methodically how you should do to find this solution.

5. ## Re: Factorisation

Originally Posted by Benjy
Thanks! Could you please explain methodically how you should do to find this solution.
Plato, he's yours.

6. ## Re: Factorisation

Originally Posted by Also sprach Zarathustra
Plato, he's yours.
No I will let you have this one.

7. ## Re: Factorisation

@ Benjy:
Notice:
$a^2-b^2=(a-b)\cdot (a+b)$

8. ## Re: Factorisation

Originally Posted by Siron
@ Benjy:
Notice:
$a^2-b^2=(a-b)\cdot (a+b)$
"methodically" $a$ and $b$ are already taken, so you, Siron should say: $x^2-y^2=(x-y)(x+y)$

9. ## Re: Factorisation

Originally Posted by Siron
@ Benjy:
Notice:
$a^2-b^2=(a-b)\cdot (a+b)$
Originally Posted by Also sprach Zarathustra
"methodically" $a$ and $b$ are already taken, so you, Siron should say: $x^2-y^2=(x-y)(x+y)$

thanks. I'm actually familiar with this one. But the one that I posted was much more complicated I think.

10. ## Re: Factorisation

In case of factorisation it's very important to know the (most important) special products and even more important if you can recognize them.