factor completely:

x^2 + 2xy + y^2 − 2xz − 2yz + z^2

(x+y-z)(x+y-z) ?

Try multiplying those out..

wat about the 2's????

To factor the given expression completely, we need to look for common factors in each term and group them accordingly. Let's go step by step:

First, let's look for common factors in the first three terms: x^2, 2xy, and y^2. The common factor is x, so we can factor out x:

x(x + 2y + y^2) - 2xz - 2yz + z^2

Next, let's look for common factors in the last three terms: -2xz, -2yz, and z^2. The common factor is -z, so we can factor out -z:

x(x + 2y + y^2) - z(2x + 2y - z)

Now we have factored out the common factors, but we can still do some simplification. Notice that we have x + 2y + y^2 in the first set of parentheses and 2x + 2y - z in the second set of parentheses. We can combine like terms within each set of parentheses:

x(x + y + y)(x + y) - z(2x + z - y)

Now we can simplify further:

x(x + y)^2 - z(2x - z + y)

And that is the completely factored form of the expression x^2 + 2xy + y^2 − 2xz − 2yz + z^2.