How do you simplify 5(x - 4)(x + 1 + i)(x - 1 - i)5(x−4)(x+1+i)(x−1−i)?
1 Answer
May 22, 2018
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