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Factor `4w^2-25` completely.

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awlgeelady | Student, Undergraduate | Honors

Posted February 22, 2013 at 8:23 PM via web

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Factor `4w^2-25` completely.

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mathlete13 | High School Teacher | (Level 2) Adjunct Educator

Posted February 22, 2013 at 8:44 PM (Answer #1)

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To factor `4w^2-25`, it is helpful to observe that both terms are perfect squares. Because the two terms are being subtracted, this expression is an instance of the special factoring pattern called difference of squares, which factors as such:

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

The values a and b are the square roots of the two terms. Therefore, in the given expression, a = 2w and b = 5. Thus, `4w^2-25` factors into (2w - 5)(2w + 5).

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