How do you simplify 5(x - 4)(x + 1 + i)(x - 1 - i)5(x4)(x+1+i)(x1i)?

1 Answer
May 22, 2018

5x^3-20x^2-10x i+40i5x320x210xi+40i

Explanation:

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

rArr5(x-4)=5x-205(x4)=5x20

((x+1)+i)((x-1)-i)larrcolor(blue)"expand using FOIL"((x+1)+i)((x1)i)expand using FOIL

=(x+1)(x-1)-i(x+1)+i(x-1)-i^2=(x+1)(x1)i(x+1)+i(x1)i2

=x^2-1-x i-i+x i-i+1toi^2=-1=x21xii+xii+1i2=1

=x^2-2i=x22i

rArr(5x-20)(x^2-2i)(5x20)(x22i)

=5x^3-10x i-20x^2+40i=5x310xi20x2+40i