(x+y-z)(x+y-z) ?
Try multiplying those out..
x^2 + 2xy + y^2 − 2xz − 2yz + z^2
Try multiplying those out..
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.