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 =

Algebra ->  Polynomials-and-rational-expressions -> 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 =       Log On


   



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) About Me  (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