SOLUTION: I would really appreciate any help you could can give me regarding the two following problems. The instructions are to Factor the polynomial. I have been able to do the others, b

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: I would really appreciate any help you could can give me regarding the two following problems. The instructions are to Factor the polynomial. I have been able to do the others, b      Log On

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Question 27810: I would really appreciate any help you could can give me regarding the two following problems. The instructions are to Factor the polynomial. I have been able to do the others, but for some reason these two have me stuck.
Factor Completely
Problem One - 64-(r+2t)^2
Problem Two - -k^2-h^2+2kh+4
Thanks in advance for your assistance

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
1) Factor:
64-%28r%2B2t%29%5E2 You should recognise this as the difference of two squares: 64+=+8%5E2 and %28r%2B2t%29%5E2
The difference of two squares can be factored:
A%5E2+-+B%5E2+=+%28A%2BB%29%28A-B%29 Appplying this to your problem:
8%5E2+-+%28r%2B2t%29%5E2+=+%288+%2B+%28r%2B2t%29%29%288+-+%28r%2B2t%29%29 = %288%2Br%2B2t%29%288-r-2t%29
2) Factor:
-k%5E2-h%5E2%2B2kh%2B4 If you rearrange this expression, you will see that it is really the difference of two squares.
4+-+%28k%5E2-2kh%2Bh%5E2%29 Factor the parentheses.
4+-+%28k-h%29%5E2 Now it's in the form of: A%5E2+-+b%5E2which will factor nicely.
4+-+%28k-h%29%5E2+=+%282+%2B+%28k-h%29%29%282+-+%28k-h%29%29 = %282%2Bk-h%29%282-k%2Bh%29
You can verify these answers by multiplying the factors to see that you get back the original expressions.
I'll leave this as an exercise for the student!