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6.2 Difference of 2 Squares List all the perfect square constants in order 1,4,9,16,25,36,49,64,81,100,121,144,169, 196,225……etc List all the perfect square variables 2 4 6 8 10 12 14 x , x , x , x , x , x , x ....etc 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? 6 4y 9 4y 6 1y 10 8y 10 25y 1 16y 156 9y = 78 3y • 78 3y Factoring the difference of two squares Rule: 2 A – 2 B = (A + B)(A – B) Ex 1: Factor: 2 9x – 25 (3x + 5 )( 3x - 5 ) Ex 2: Factor: 6 2 y – 9x 3 (y + 3 3x)(y - 3x) Ex 3:Factor: 6 2 4y – 9x 3 (2y + 3 3x)(2y - 3x) 5x Ex 4: Factor: 4 25x - 9 2 3 5x 3 2 Homework Page 268 (1-28) all Day 2” 6.2 Difference of Two Squares Three Important Ideas 1.) Anytime there is a + sign with two positive numbers you can not take the difference of two squares. Ex: (y2 + 25) cannot be factored. But….. If you have a + sign with one negative and one positive number you can rearrange it to look like a difference of two squares Ex: -25+x² x²+-25 x²-25 (x+5)(x-5) Three Important Ideas 2.) Factor out any common terms first, then factor as the difference of two squares if possible Ex : Factor: 32x2 – 50y2 2(16x2 – 25y2) 2(4x + 5y) (4x - 5y) Ex : Factor: 9x4 + 36 9( x 4) 4 Three Important Ideas 3.) Factor completely!!! Sometimes, the minus binomial will be another difference of two squares. Keep factoring until it is not another difference of two squares! Ex: Factor 4 81x – 1 (9x2 + 1) (9x2 – 1) (9x² +1) (3x + 1) (3x - 1) Ex Factor: 16x4 – y8 (4x2 + y4) (4x2 – y4) (4x2 + y4)(2x + y2) (2x – y2) Homework Page 268 (30-62) even