SOLUTION: bTO THE POWER OF 2 - 2bc+ cTO THE POWER OF 2 =

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Question 84712: bTO THE POWER OF 2 - 2bc+ cTO THE POWER OF 2 =
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
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b%5E2+-+2bc+%2B+c%5E2
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I think what you are after is finding the factors of this trinomial. The first term b%5E2
can be factored into b times b. Therefore you can set up two pairs of parentheses and use b
as the first term for both ... as in (b + _ )*(b + _ ).
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The last term in the given trinomial is c%5E2 and it can be factored in a couple of
ways ... it can be +c times +c or -c times -c. Both of these products will be positive.
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But notice that the middle term of the trinomial is negative. This tells you that the factors
you need to use for the last term and negative c times negative c in order to generate
a -2bc in the trinomial.
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This means that the pair of factors must be (b - c)*(b - c) and since both factors are
the same, you can write this as %28b+-+c%29%5E2.
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So the answer to factoring the given trinomial is that it factors to %28b-c%29%5E2.
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Hope this is what you were looking for. If not, re-post your problem and let us know what
you are being asked to do. Cheers!