Warm Up ~ 10-4~Factoring Sums and Differences of Squares Factor each polynomial: 1.x x Factor each perfect square. If not a perfect square, write not a perfect square: 3. 9x 2 +6x x 2 -8x+1 Factor the polynomial using a special case or write not special case: x 2 -64y 2

Lesson 10-5 Factoring Perfect Square Trinomials By: Rachel Geiger and Jessica Solinski

Lesson 10-5 Factoring Perfect Square Trinomials The goal of this lesson is to determine a pattern that is a perfect square. When writing out the factors, the pattern you should see is that it will be able to be written in the form:The goal of this lesson is to determine a pattern that is a perfect square. When writing out the factors, the pattern you should see is that it will be able to be written in the form: (a + b) 2 = a 2 + 2ab + b 2

The Basics You have already factored trinomials before, so it’s exactly the same thing. However, you are looking to see if the trinomials are perfect squares. If the trinomials are not perfect squares, just write “not a perfect square”.

Breaking It Down Step 1: Ask yourself three questions: ~ Is the first term a perfect square? ~ Is the last term a perfect square? ~ Is the middle term the product of twice the square roots of the last and first terms? To answer these questions, you need to find the square root of each term. Step 2: If you answered yes to all of them, it is a perfect square. Now you have to write it in the form: (a + b) 2 = a 2 + 2ab + b 2 and simplify.

Applying the Steps Example: 4y yz + 81z 2 Step 1: Is the first term a perfect square? (Square root) 4y 2 = (2y) 2  Is the last term a perfect square? (Square Root) 81z 2 = (9z) 2  Is the middle term twice the product of 2y and 9z? (The square roots) 36yz = 2(2y)(9z)  Step 2: We have determined that 4y yz + 81z 2 is a perfect square trinomial because we answered yes to all of the questions. Now, we have to write it out in the form (a + b) 2 = a 2 + 2ab + b 2 4y yz + 81z 2 = (2y) 2 + 2(2y)(9z) + (9z) 2 = (2y + 9z) 2

Practice Problems 9n n 9n n = 9n 2 – n 2 = (3n) 2 49 = (7) n = -2 (3n)(7) Not perfect square

More Practice 4x 2 – 12x x 2 – 12x + 36 = 4x 2 – x 4x 2 = (2x) 2 12x = does not have square root ~so this is not a perfect square~