Factorize x^2 - 2xz - 2xy + 4yz

Question

whpalmer4 · Answer

Factor by grouping terms and factoring separately:
$$(x^2-2xz) - (2xy - 4yz)$$$$x(x-2z) - 2y(x -2z)$$
Can you factor that?  Think distributive property in reverse...

4meisu · Answer

So I would have to factorize x(x-2z)?

whpalmer4 · Answer

No, think of (x-2z) as a single item:
We'll write $a = x-2z$
Now our expression is 
$$xa - 2ya$$
Can you factor that?

4meisu · Answer

a(x - 2y)

whpalmer4 · Answer

Right!  Now plug in the value of a and you have...

4meisu · Answer

I'm sorry, I got confused. Plug in the value of a with what? (Yes, I am super bad at Math)

whpalmer4 · Answer

We simplified the recognition that you could factor $$x(x-2z) - 2y(x-2z)$$ by writing $a = x-2z$ and then factoring it.  Now we need to replace a with $x-2z$:
$$a(x-2y) = (x-2z)(x-2y)$$

whpalmer4 · Answer

You're not used to factoring out something like (x-2z), you're used to factoring out things like x, or 4.  It takes a bit of practice to start spotting the more complicated factors.

whpalmer4 · Answer

This procedure I went through is called factoring by grouping.

4meisu · Answer

Aaaah okay. Thank you!