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>> The first thing we need to do, as always, is think about what adds to equal
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4, and multiplies to equal 4 times 1, or 4? In this case, our numbers are 2 and
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2. So instead of 4x, we can write 2x plus 2x, and of course the rest of the
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expression as well. Then something interesting happens when we try to factor the
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first two terms and the second two terms. The first two are pretty normal, we
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pull out a 2x from the 4x squared plus 2x, but then when we get to 2x plus 1
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Well there are no common factors that 2x and 1 have aside from 1. So that's
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exactly what we write, 1. And then the last two terms, 2x plus 1. Conveniently,
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this still works out perfectly and we get 2x plus 1 times 2x plus 1. Which we
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can also write as 2x plus 1 the quantity squared.