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Factor: 4a^2c^2 - (a^2-b^2+c^2)^2

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spock1 | Student, Undergraduate | (Level 2) Honors

Posted May 7, 2012 at 2:49 AM via web

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Factor: 4a^2c^2 - (a^2-b^2+c^2)^2

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 7, 2012 at 3:31 AM (Answer #1)

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The expression 4a^2c^2 - (a^2-b^2+c^2)^2 has to be factored.

4a^2c^2 - (a^2 - b^2 + c^2)^2

=> (2ac)^2 - (a^2 - b^2 + c^2)^2

=> (2ac - a^2 + b^2 - c^2)(2ac + a^2 - b^2 + c^2)

=> (b^2 - (a^2 - 2ac + c^2))((a^2 + 2ac + c^2) - b^2)

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

=> (b - a + c)(b + a - c)(a + b + c)(a - b + c)

The factorized form of 4a^2c^2 - (a^2-b^2+c^2)^2 is (b - a + c)(b + a - c)(a + b + c)(a - b + c)

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