Question #84ae9

1 Answer
Nam D.
Jan 2, 2018

x^8-4x^7-2x^6+20x^5+x^4-40x^3-8x^2+32x+16x8−4x7−2x6+20x5+x4−40x3−8x2+32x+16

Explanation:

First, rearrange (2+x-x^2)^4(2+x−x2)4 into (-x^2+x+2)^4(−x2+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)(−x2+x+2)4=(−x2+x+2)(−x2+x+2)(−x2+x+2)(−x2+x+2)

=(x^4-2x^3-3x^2+4x+4)(-x^2+x+2)(-x^2+x+2)=(x4−2x3−3x2+4x+4)(−x2+x+2)(−x2+x+2)

=(-x^6+3x^5+3x^4-11x^3-6x^2+12x+8)(-x^2+x+2)=(−x6+3x5+3x4−11x3−6x2+12x+8)(−x2+x+2)

=x^8-4x^7-2x^6+20x^5+x^4-40x^3-8x^2+32x+16=x8−4x7−2x6+20x5+x4−40x3−8x2+32x+16

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