Question #84ae9

1 Answer
Nam D.
Jan 2, 2018

#x^8-4x^7-2x^6+20x^5+x^4-40x^3-8x^2+32x+16#

Explanation:

First, rearrange #(2+x-x^2)^4# into #(-x^2+x+2)^4#. Then we have:

#(-x^2+x+2)^4=(-x^2+x+2)(-x^2+x+2)(-x^2+x+2)(-x^2+x+2)#

#=(x^4-2x^3-3x^2+4x+4)(-x^2+x+2)(-x^2+x+2)#

#=(-x^6+3x^5+3x^4-11x^3-6x^2+12x+8)(-x^2+x+2)#

#=x^8-4x^7-2x^6+20x^5+x^4-40x^3-8x^2+32x+16#

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