How does $ x^{2} -xz- y^{2}+yz $ become $(x-y)(x+y-z)$? I need some help in simplifying this expression. I want sums of terms into products instead.
$$ x^{2} -xz- y^{2}+yz $$
The answer is supposed to be:
$$(x-y)(x+y-z)$$
I just don't understand how, I tried doing completing the square with no success. I can't find anything to factor out that's common amongst all the terms.
Factorize $x^2-y^2$ and $yz - xz$ separately to find some like terms. $x^2-y^2$ becomes $(x-y)(x+y)$ and $yz-xz$ becomes $z(y-x)$. You can convert $z(y-x)$ to $-z(x-y)$. Now we can take $(x-y)$ common, so we get $(x-y)(x+y-z)$. Hence, we get our answer. Hope it helps
Writing your expression $(x^2-y^2)+(yz-xz)$ make things clearer. Indeed, we have:
$$x^2-y^2=(x-y)(x+y)$$
$$yz-xz=(y-x)z=(x-y)(-z)$$
Therefore, your expression is equal to $(x-y)(x+y)+(x-y)(-z)$. Can you figure out the last step?