SOLUTION: what is the complete factor the binomial 64x squared minus 100 y squared

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Question 444926: what is the complete factor the binomial 64x squared minus 100 y squared
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
We have 64x%5E2+-+100y%5E2
Notice that we have a difference of squares and recall the formula for the difference of squares: %28a%5E2+-b%5E2%29+=+%28a%2Bb%29%28a-b%29.
Also notice that 64x%5E2+=+%288x%29%5E2 and 100y%5E2+=+%2810y%29%5E2 This is why they are perfect squares.
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So following the formula 64x%5E2-100y%5E2+=+%288x%29%5E2+-+%2810y%29%5E2+=+%288x%2B10y%29%288x-10y%29
Notice that a "2" is common in each factor, so we can factor out a 2.
2%284x%2B5y%29+%2A+2%284x-5y%29. Now collect 2*2 to get 4 and we have our answer.
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4%2A%284x%2B5y%29%2A%284x-5y%29
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If you'd like, FOIL this out to check.