8-9 Notes for Algebra 1 Perfect Squares

8-9 pg. 527 16-46, 63-75(x3)

Perfect Square Trinomials The first term is a perfect square, the last term is a perfect square, and the middle term is found by doubling the product of the square root of the 1st term and the square root of the last term. 𝑎 2 +2𝑎𝑏 +𝑏 2 = 𝑎+𝑏 𝑎+𝑏 = 𝑎+𝑏 2 𝑎 2 −2𝑎𝑏 +𝑏 2 = 𝑎−𝑏 𝑎−𝑏 = 𝑎−𝑏 2

Example 1: Recognize and Factor Perfect Square Trinomials Determine whether each trinomial is a perfect square trinomial. Write yes or no. If it is a perfect square, factor it. 1.) 25𝑥 2 −30𝑥+9 2.) 49𝑦 2 +42𝑦+36

Example 1: Recognize and Factor Perfect Square Trinomials Determine whether each trinomial is a perfect square trinomial. Write yes or no. If it is a perfect square, factor it. 1.) 25𝑥 2 −30𝑥+9 2.) 49𝑦 2 +42𝑦+36 Yes, 5𝑥−3 2 No

Example 2: solve equations with repeated factors Factor Completely. 1.) 6𝑥 2 −96 2.) 16𝑦 2 +8𝑦−15

Example 2: Factor Completely

Example 3: Solve Equations with Repeated factors

Example 3: Solve Equations with Repeated factors

Square root property If 𝑥 2 =𝑛, then 𝑥=± 𝑛

Example 4: Use the Square Root Property Solve each equation. Check the results. 1.) 𝑏−7 2 =36 2.) 𝑥+9 2 =8

Example 4: Use the Square Root Property Solve each equation. Check the results. 1.) 𝑏−7 2 =36 𝑏=1, 13 2.) 𝑥+9 2 =8 𝑥=−9±2 2 𝑥≈−11.8, −6.2