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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!!!. x 2. x 5. x 6. x 9.
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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!!!
x2 x5 x6 x9 9 is a Perfect Square because 3 • 3 = 9. Can you find the other perfect squares? 12 9 10 16
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 4y6 = (2y3)(2y3) 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)
5 3x 3x 5 Factor: 9x2 – 25 ( + )( - )
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:32x2 – 50y2 2(16x2 – 25y2) 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.
