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What are the factors of(4x+6)^2 - (2y-2)^2?

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medausza | Student, College Freshman | (Level 1) eNoter

Posted July 24, 2011 at 8:35 PM via web

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What are the factors of(4x+6)^2 - (2y-2)^2?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted July 24, 2011 at 8:39 PM (Answer #1)

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This is a difference of two squares that returns the product:

a^2 - b^2 = (a-b)(a+b)

Let a = 4x + 6 and b = 2y - 2

a - b = 4x + 6 - 2y + 2 = 4x - 2y + 8

a + b = 4x + 6 + 2y - 2 = 4x + 2y + 4

The requested factors are:(4x+6)^2 - (2y-2)^2 = (4x - 2y + 8)(4x + 2y + 4).

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted July 26, 2011 at 1:37 PM (Answer #2)

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(4x + 6)^2 - (2y - 2)^2

This shows the Difference of Squares Pattern.

Allow a to represent (4x + 6).

Allow b to represent (2y - 2)

According to the Difference of Squares Pattern:

a^2 - b^2 = (a + b)(a - b)

Therefore...

(4x + 6)^2 - (2y - 2)^2 = (4x + 6 + 2y + 2)(4x + 6 - 2y + 2)

Simplified factors:  (4x + 2y + 8)(4x - 2y + 8)

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