Question 32440
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