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Factorizing quadratic equations

Hi there again
Could you please show me the solutions of factorising the following equations

4x^2-3y^2-(x^2-x+y)

and

ab(z^2+1)-z(a^2+b^2)

It's not that I'm lazy and want yous to do it for me... it's just difficult and my teacher won't give me a straight answer :mad:
Thanks

Quote:

Originally Posted by sim0nz12345

Hi there again
Could you please show me the solutions of factorising the following equations

$4x^{2}-3y^{2}-(x^{2}-x+y)$

First, simplify. See the x^2 terms. Rewrite as:

$3x^{2}-3y^{2}+x-y$

Factor out 3:

$3(x^{2}-y^{2})+(x-y)$

Now, see the difference of two squares in there?

Quote:

$ab(z^2+1)-z(a^2+b^2)$

The trick with these things is to rearrange so you have something familiar you can work with.

Expand out and see what you can do.

$abz^{2}+ab-a^{2}z-b^{2}z$

This can be written as :

$zb(az-b)-a(az-b)$ , can't it?

See what's in the parentheses. It's the same. That's a clue.

You can finish now?

Cool
Thank you very much
Much appreciated