SOLUTION: Please factor completely the following polynomials: 1) (a-b)2(squared) - 4(c-d)2 (squared) 2) 6(x-y)2 (squared) + 23(x-y) - 4 Simplify and express answers using positive expon

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please factor completely the following polynomials: 1) (a-b)2(squared) - 4(c-d)2 (squared) 2) 6(x-y)2 (squared) + 23(x-y) - 4 Simplify and express answers using positive expon      Log On


   

Question 1757: Please factor completely the following polynomials:
1) (a-b)2(squared) - 4(c-d)2 (squared)
2) 6(x-y)2 (squared) + 23(x-y) - 4
Simplify and express answers using positive exponents only.
1) 5
----
4x-9 (exponent -9)
2) m-11 (exponent -11)
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m-5 (exponent -5)
3) (2a-3 (exponent 3))2 (squared)
Thank You.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
1. Given x%5E2+-+4y%5E2, this factorises to %28x%2B2y%29%28x-2y%29. So similarly, %28a-b%29%5E2+-+4%28c-d%29%5E2 becomess %28%28a-b%29%2B2%28c-d%29%29%28%28a-b%29-2%28c-d%29%29
2. think of 6z%5E2+%2B+23z+-+4. This factorises to %286z-1%29%28z%2B4%29...you just have to mess around with the possibilities and eventually find the correct pairing. There is no "secret" here, just looking at the numbers.
Hence, we then get +%286%28x-y%29-1%29%28x-y%2B4%29+
3. %285x%5E9%29%2F4
4. m%5E%28-6%29 becomes 1%2Fm%5E6
5. %282a%5E%28-3%29%29%5E2 becomes 4a%5E%28-6%29 which becomes 4%2Fa%5E6
cheers
Jon.