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Old 2003-08-30, 17:56   #5
axn
 
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Jun 2003

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Default Re: Factoring Problem

Quote:
Originally Posted by asdf
I'm having trouble with this problem:

Factor: (4)(a^2)(c^2) - (a^2 - b^2 + c^2)^2

Thanks
Soln: (I am omitting the * for multiplication)

(4)(a^2)(c^2) - (a^2 - b^2 + c^2)^2

==> X^2 - Y^2, where X = 2ac and Y = (a^2 - b^2 + c^2)

==> (X+Y)(X-Y)

==> (2ac + a^2 - b^2 + c^2)(2ac - a^2 + b^2 - c^2)

==> [(a+c)^2 - b^2] [b^2 - (a-c)^2]

==>[(a+c+b)(a+c-b)] [(b+a-c)(b-a+c)]
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