SOLUTION: I have another problem that I need some help. My first response was extremely helpful. Here's my problem: (x^2-3x+1)^2 - (x^2+5x+1)^2 What we have so far is: (x^2-3x+1)^2 =

Question 32440: I have another problem that I need some help. My first response was extremely helpful.
Here's my problem:
(x^2-3x+1)^2 - (x^2+5x+1)^2
What we have so far is: (x^2-3x+1)^2 = x^4-6x^3+11x^2-6x+1.
Confused about how to handle the subtraction sign for the following expression. Should it be distributed out throughout the problem? Thanks very much for your help!
Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
Using the property a^2 - b^2 = (a+b)(a-b),
(x^2-3x+1)^2 - (x^2+5x+1)^2
= [x^2-3x+1)+(x^2+5x+1)][(x^2-3x+1)-(x^2+5x+1)]
= (2x^2+2x+2)(-8x)
= -16x(x^2+x+2)
= -16x^3-16x^2-32x

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