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Factoring question

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Factoring question

by afr114 » Tue Oct 22, 2013 7:31 am
Can someone explain the reason behind why the following equation turns into this (x+5)(x-1)^2:

x(x-1)^2 +5(x-1)^2

I get that the coefficents are added into (x+5) but what exactly happens to (x-1)^2*(x-1)^2? Or am I not factoring it correctly?
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by Brent@GMATPrepNow » Tue Oct 22, 2013 7:49 am
afr114 wrote:Can someone explain the reason behind why the following equation turns into this (x+5)(x-1)^2:

x(x-1)^2 +5(x-1)^2

I get that the coefficents are added into (x+5) but what exactly happens to (x-1)^2*(x-1)^2? Or am I not factoring it correctly?
Let's look at some similar examples first.

3x + 4x = (3+4)x = 7x
8y² - 3y² = (8-5)y² = 3y²

So, here we have
x(x-1)² + 5(x-1)² = (x+5)(x-1)²

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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