Find Equivalent Expressions to (x-y)²: Perfect Square Expansion

When you FOIL $(x-y)(x-y)$, you get two negative terms: $-xy$ and $-yx$. Adding them gives $-2xy$, which is why the middle term is negative!

$(x+y)^2 = x^2 + 2xy + y^2$ has a positive middle term, while $(x-y)^2 = x^2 - 2xy + y^2$ has a negative middle term. The sign of the binomial determines the middle term's sign!

Yes! The formula $(a-b)^2 = a^2 - 2ab + b^2$ is faster once memorized. But understanding why it works through FOIL helps you remember it correctly and avoid sign errors.

You confused perfect squares with difference of squares! Remember: $x^2 - y^2 = (x+y)(x-y)$ factors into two different binomials, while $(x-y)^2$ is the same binomial multiplied by itself.

Pick simple values like $x=3, y=1$. Then $(3-1)^2 = 4$, and your answer $3^2 - 2(3)(1) + 1^2 = 9 - 6 + 1 = 4$. They match!