Solve the Quadratic Expression: (x+3)² + (x-3)²

Great observation! The middle terms $+6x$ and $-6x$ are opposites that cancel each other out. This happens because one binomial has $(x+3)$ and the other has $(x-3)$ - the signs are opposite!

Yes! When you have $(x+a)^2$ and $(x-a)^2$, both give $a^2$ as the constant term. Here, both give $3^2 = 9$, so we get $9 + 9 = 18$.

Absolutely! FOIL works perfectly: $(x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9$. However, memorizing the perfect square patterns makes you faster and less prone to arithmetic errors.

If you had something like $(x+2)^2 + (x-5)^2$, the middle terms won't cancel because they're not opposites. You'd get terms like $4x$ and $-10x$, leaving $-6x$ in your final answer.

Each squared binomial contributes one $x^2$ term, so $x^2 + x^2 = 2x^2$. This pattern holds for any $(x+a)^2 + (x-a)^2$ - you'll always get $2x^2$!