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Factor \((x^2+y^2-z^2)^2-4x^2y^2\) as the product of four polynomials of degree 1, each of which has a positive coefficient of \(x\).

 

So far, I've factored it out to be \((-x-y+z)(x-y+z)(-x+y+z)(x+y+z)\)but how am I supposed to factor it so that way \(x\) is always positive? Does anyone have some tips/walkthroughs on how to solve this?

 

Thanks

 Jan 25, 2020
 #1
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You can take these two factors:  (-x - y + z)(-x + y + z)

and factor -1 out of these:          [-1(x + y - z)]·[-1(x - y - z)]

Rewrite:                                     (-1)(-1)·(x + y - z)(x - y - z)

to get:                                               (x + y - z)(x - y - z)

 Jan 25, 2020

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