match each expression to its equivalent standard form

Accepted Solution

Answer:(x+1+i)(x+1-i) goes with x^2+2x+2(x+2i)(x-2i) goes with x^2+4(x-2+2i)(x-2-2i) goes with x^2-4x+8Step-by-step explanation:(x+1+i)(x+1-i)(x+[1+i])(x+[1-i])Use foil.First: x(x)=x^2Outer: x(1+i)=x+ixInner: x(1-i)=x-ixLast: (1+i)(1-i)=1-i^2 since 1+i and 1-i are conjugates__Add together to get: x^2+2x+1-i^2We can actually simplify this because i^2=-1So x^2+2x+1-i^2=x^2+2x+1-(-1)=x^2+2x+2(x+2i)(x-2i)These are conjugates so just do first and last of foil. First: x(x)=x^2Last: 2i(-2i)=-4i^2=-4(-1)=4==Adding together gives x^2+4(x-2+2i)(x-2-2i)(x+[-2+2i])(x+[-2-2i])This is similar to first.Foil time!First: x(x)=x^2Outer: x(-2-2i)=-2x-2ixInner: x(-2+2i)=-2x+2ixLast: (-2-2i)(-2+2i)=4-4i^2 (multiplying conjugates again)==Add together giving us x^2-4x+4-4i^2This can be simplified since i^2=-1.So applying this gives us x^2-4x+4-4(-1)=x^2-4x+4+4=x^2-4x+8