Factoring a Difference of Squares: Solve x^2 - 49 = (x-_—)(x+_—)

Ask yourself: what number times itself equals this? For 49, think $7 \times 7 = 49$, so $\sqrt{49} = 7$. Common perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

The difference of squares formula $a^2 - b^2 = (a - b)(a + b)$ always uses the same values with opposite signs. Since we have $x^2 - 7^2$, both blanks must be 7.

Think about reversing multiplication! When you multiply $(x - 7)(x + 7)$, the middle terms $+7x$ and $-7x$ cancel out, leaving only $x^2 - 49$.

Yes! Multiply out $(x - 7)(x + 7)$: First terms give $x^2$, outer and inner terms give $+7x - 7x = 0$, last terms give $-49$. Result: $x^2 - 49$ ✓

Then it's not a difference of squares! You can only use this method when both terms are perfect squares. For example, $x^2 - 50$ can't be factored this way since 50 isn't a perfect square.