Bellringer part two Simplify (m – 4) 2. (5n + 3) 2.

Determine the pattern … = 1 2 = 2 2 = 3 2 = 4 2 = 5 2 = 6 2 These are perfect squares! You should be able to list at least the first 15 perfect squares in 30 seconds…

GO!!! Perfect squares 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 How far did you get?

Perfect Square Trinomial Ax 2 + Bx + C Clue 1: A & C are positive, perfect squares. Clue 2: B is the square root of A times the square root of C, doubled. If these two things are true, the trinomial is a Perfect Square Trinomial and can be factored as (x + y) 2 or (x – y) 2.

General Form of Perfect Square Trinomials x 2 + 2xy + y 2 = (x + y) 2 or x 2 – 2xy + y 2 = (x - y) 2 Note: When factoring, the sign in the binomial is the same as the sign of B in the trinomial.

Just watch and think. Ex) x x + 36 What ’ s the square root of A? of C? Multiply these and double. Does it = B? Then it ’ s a Perfect Square Trinomial! Solution: (x + 6) 2 Ex) 16a 2 – 56a + 49 Square root of A? of C? Multiply and double… = B? Solution: (4a – 7) 2

Ex. 1: Determine whether each trinomial is a perfect square trinomial. If so, factor it. 1. y² + 8y y² - 30y + 10

Example 2: Factoring perfect square trinomials. 1) x 2 + 8x + 162) 9n n ) 4z 2 – 36z ) 9g² +12g - 4

4)25x² - 30x + 9 5)x² + 6x - 9 6) 49y² + 42y ) 9m³ + 66m² - 48m

Review: Multiply (x – 2)(x + 2) First terms: Outer terms: Inner terms: Last terms: Combine like terms. x 2 – 4 x-2 x +2 x 2 +2x -2x -4 This is called the difference of squares. x2x2 +2x -2x -4 Notice the middle terms eliminate each other!

Difference of Squares a 2 - b 2 = (a - b)(a + b) or a 2 - b 2 = (a + b)(a - b) The order does not matter!!

4 Steps for factoring Difference of Squares 1. Are there only 2 terms? 2. Is the first term a perfect square? 3. Is the last term a perfect square? 4. Is there subtraction (difference) in the problem? If all of these are true, you can factor using this method!!!

1. Factor x When factoring, use your factoring table. Do you have a GCF? Are the Difference of Squares steps true? Two terms? 1 st term a perfect square? 2 nd term a perfect square? Subtraction? Write your answer! No Yes x 2 – 25 Yes ( )( )5xx+5 -

2. Factor 16x When factoring, use your factoring table. Do you have a GCF? Are the Difference of Squares steps true? Two terms? 1 st term a perfect square? 2 nd term a perfect square? Subtraction? Write your answer! No Yes 16x 2 – 9 Yes (4x )(4x )3+3 -

When factoring, use your factoring table. Do you have a GCF? Are the Difference of Squares steps true? Two terms? 1 st term a perfect square? 2 nd term a perfect square? Subtraction? Write your answer! (9a )(9a )7b Factor 81a 2 – 49b 2 No Yes 81a 2 – 49b 2 Yes

Factor x 2 – y 2 1.(x + y)(x + y) 2.(x – y)(x + y) 3.(x + y)(x – y) 4.(x – y)(x – y) Remember, the order doesn’t matter!

When factoring, use your factoring table. Do you have a GCF? 3(25x 2 – 4) Are the Difference of Squares steps true? Two terms? 1 st term a perfect square? 2 nd term a perfect square? Subtraction? Write your answer! 3(5x )(5x ) Factor 75x 2 – 12 Yes! GCF = 3 Yes 3(25x 2 – 4) Yes

Factor 18c 2 + 8d 2 1.prime 2.2(9c 2 + 4d 2 ) 3.2(3c – 2d)(3c + 2d) 4.2(3c + 2d)(3c + 2d) You cannot factor using difference of squares because there is no subtraction!

Factor m 2 Rewrite the problem as 4m 2 – 64 so the subtraction is in the middle! 1.prime 2.(2m – 8)(2m + 8) 3.4(-16 + m 2 ) 4.4(m – 4)(m + 4)

Ex. 3: Factor completely. 2x² + 18 c² - 5c + 6 5a³ - 80a 8x² - 18x - 35

Ex. 3: Solve each equation. 3x² + 24x + 48 = 0 49a² + 16 = 56a

z² + 2x + 1= 16 (y – 8)² = 7