Question

Match each expression to its equivalent standard form.

A. x^2 + x + 2
B. x^2 + 2x + 2
C. x^2 + 4
D. x^2 - 4x + 8
E. x^2 +16
F. x^2- 4x -4
1. (x + 2i)(x -2i)
2. (x - 2 + 2i)(x - 2 - 2i)
3. (x + 1 + I)(x + 1 - I)

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`