Question

Match each expression to its equivalent standard form.

Answer 1

Let's expand the products they are all in the form

$(a+b)(a-b)=a^2-b^2$

For the first one we have a=x and b=2i:

$(x+2i)(x-2i)=x^2-(2i)^2=x^2+4$

For the second one we have a=x-2 and b=2i:

$(x-2+2i)(x-2-2i)=(x-2)^2-(2i)^2 = x^2-4x+4+4=x^2-4x+8$

For the third one we have a=x+1 and b=i:

$(x+1+i)(x+1-i)=(x+1)^2-i^2=x^2+2x+1+1=x^2+2x+2$