Factoring Quadratics 09B9C7

1. **State the problem:** Match each quadratic expression to its factored form. 2. **Recall factoring formulas:** - Difference of squares: $$x^2 - y^2 = (x+y)(x-y)$$ - Perfect square trinomial: $$x^2 \pm 2xy + y^2 = (x \pm y)^2$$ 3. **Match each expression:** - $a^2 - 49$ is a difference of squares: $$a^2 - 7^2 = (a+7)(a-7)$$ - $a^2 + 14a + 49$ is a perfect square trinomial: $$a^2 + 2 \cdot a \cdot 7 + 7^2 = (a+7)^2$$ - $a^2 - 14a + 49$ is a perfect square trinomial: $$a^2 - 2 \cdot a \cdot 7 + 7^2 = (a-7)^2$$ - $a^2 + 49$ cannot be factored over the reals (sum of squares), so it is **prime**. 4. **Final matches:** - $a^2 - 49 \to (a+7)(a-7)$ - $a^2 + 14a + 49 \to (a+7)^2$ - $a^2 - 14a + 49 \to (a-7)^2$ - $a^2 + 49 \to$ prime 5. **Explanation:** - Difference of squares factors into two binomials with opposite signs. - Perfect square trinomials factor into the square of a binomial. - Sum of squares is prime over real numbers. This completes the matching.