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Show that (2x −1)^2 − (x − 3)^2 can be simplified to (x + 2)(3x − 4).

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christiano-cr7 | Salutatorian

Posted August 3, 2013 at 10:33 AM via web

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  1. Show that (2x −1)^2 − (x − 3)^2 can be simplified to (x + 2)(3x − 4).

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llltkl | College Teacher | Valedictorian

Posted August 3, 2013 at 10:49 AM (Answer #1)

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To simplify `(2x-1)^2-(x-3)^2` ,

apply the formula `a^2-b^2=(a-b)(a+b)` . So, we get:

`(2x-1)^2-(x-3)^2`

`={2x-1-(x-3)}(2x-1+x-3)`

`=(2x-1-x+3)(2x-1+x-3)`

`=(x+2)(3x-4)`

Therefore, the simplified form of `(2x-1)^2-(x-3)^2` is `(x+2)(3x-4)` .

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