SOLUTION: Factoring: a)16b^2c^2-4(b^2+c^2-a^2) b)(x^2+4y^2-20)^2-16(xy-4)^2 I have tried some ways but could not solve this

Algebra ->  Rational-functions -> SOLUTION: Factoring: a)16b^2c^2-4(b^2+c^2-a^2) b)(x^2+4y^2-20)^2-16(xy-4)^2 I have tried some ways but could not solve this      Log On


   

Question 1119606: Factoring:
a)16b^2c^2-4(b^2+c^2-a^2)
b)(x^2+4y^2-20)^2-16(xy-4)^2
I have tried some ways but could not solve this
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Factoring:
a)16b^2c^2-4(b^2+c^2-a^2)
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b)(x^2+4y^2-20)^2-16(xy-4)^2
Same here. Some "simplification" might be possible after using the difference of squares, but Step 1 is the difference of squares.
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= %28%28x%5E2%2B4y%5E2-4%29-4xy%29%2A%28%28x%5E2%2B4y%5E2-36%29%2B4xy%29
= %28x%5E2%2B4y%5E2-4-4xy%29%2A%28x%5E2%2B4y%5E2-36%2B4xy%29
= %28x%5E2-4xy%2B4y%5E2-4%29%2A%28x%5E2%2B4xy%2B4y%5E2-36%29
Now each of the 4nomials can be factored.
= %28%28x-2y%29%5E2-4%29%2A%28%28x%2B2y%29%5E2-36%29
= %28x-2y-2%29%28x-2y%2B2%29%2A%28x%2B2y-6%29%2A%28x%2B2y%2B6%29
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Other than knowing about the difference of squares, it's just careful bookkeeping.
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Look up difference of 2 cubes, also.