6.2 Difference of 2 Squares Goal: To be able to recognize and completely factor the difference of two squares Remember to factor out a common factor before.

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6.2 Difference of 2 Squares Goal: To be able to recognize and completely factor the difference of two squares Remember to factor out a common factor before you see if it is the difference of two squares or not!!!

9 is a Perfect Square because 3 • 3 = 9 9 is a Perfect Square because 3 • 3 = 9. Can you find the other perfect squares? 12 9 10 16 x2 x5 x6 x9

A “term” (such as 9x4) is a Perfect Square if: The coefficient (9) is a perfect square, and The variable has an even number for an exponent. To take the square of an even exponent divide by 2

Is this term a perfect Square? 4y6 = (2y3)(2y3) 4y6 4y9 16y1 8y10 25y10 9y156 1y6 = 3y78 • 3y78

Are both terms perfect Squares? 4y6 – 9x2 y6 – 9x8 8y6 – 25x2 9y6 – 4x2y8

Factoring the difference of two squares (A + B)(A – B) = A2 – B2 A2 – B2 = (A + B)(A – B) = (y + 3)(y – 3) y2 – 9 m2 – 64 = (m + 8)(m – 8)

Factor: 9x2 – 25 ( + )( - ) 5 3x

Factor: y6 – 9x2 (y3 + 3x)(y3 - 3x)

Factor: 4y6 – 9x2 (2y3 + 3x)(2y3 - 3x)

Three more “notes” (y2 + 25) cannot be factored. Factor out any common terms first, then continue. 20y6 – 5  5(4y6 – 1) Factor completely. 81x4 – 1  (9x2 + 1) (9x2 – 1) (9x² +1) (3x + 1) (3x - 1)

Factor completely: 25x4 - 9

Factor completely: 32x2 – 50y2 2(4x + 5y) (4x - 5y)

Factor completely: 16x4 – y8 (4x2 + y4) (4x2 – y4) (4x2 + y4)(2x + y2) (2x – y2)

Factor completely: 9x4 + 36 Cannot be factored

Closing.. To factor the difference of 2 squares: Factor out a common factor If there is subtraction of two squares, take the square root of each one + and one – Check to see if the - of your final answer is not another difference of two squares.

Assignment: Page 268 10-48 even