How do you simplify 5(x - 4)(x + 1 + i)(x - 1 - i)5(x−4)(x+1+i)(x−1−i)?

1 Answer
Jim G.
May 22, 2018

5x^3-20x^2-10x i+40i5x3−20x2−10xi+40i

Explanation:

"expand the factors in pairs and multiply the expansions"expand the factors in pairs and multiply the expansions

rArr5(x-4)=5x-20⇒5(x−4)=5x−20

((x+1)+i)((x-1)-i)larrcolor(blue)"expand using FOIL"((x+1)+i)((x−1)−i)←expand using FOIL

=(x+1)(x-1)-i(x+1)+i(x-1)-i^2=(x+1)(x−1)−i(x+1)+i(x−1)−i2

=x^2-1-x i-i+x i-i+1toi^2=-1=x2−1−xi−i+xi−i+1→i2=−1

=x^2-2i=x2−2i

rArr(5x-20)(x^2-2i)⇒(5x−20)(x2−2i)

=5x^3-10x i-20x^2+40i=5x3−10xi−20x2+40i

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