# What is (x+2i) x (x-2i)?

Updated on August 6, 2022

math problem. i have to multiply the binomials together, (x+2i) times (x-2i).

HOW?!

• (x+2i)(x-2i)

= x(x-2i) + 2i(x-2i)

= x^2 – 2ix + 2ix -4i^2

= x^2 – 4(-1)

= x^2 + 4

• F.O.I.L. = First Outer Inner Last

First = x * x = x^2

Outer = x * -2i = -2ix

Inner = 2i * x = 2ix

Last = 2i * -2i = -4i^2 = -4(-1) = 4

x^2 – 2ix + 2ix + 4 = x^2 + 4

• in case you distribute from the beginning up, the equation could in basic terms be x+2 • x-2 • x+2i • x -2i. So, it fairly is 4 x’s, and in case you upload togeher each and all the +2s and -2s, youd have 0. (+2+-2=0. And +2i+-2i=0. they cancel eachother out) so which you basically have the 4 x. So the equation simplified is 4x. in basic terms look at each and all the 2s. They cancel eachother out, and your left with basically the x’s.

• X 2i

• Use the formula

( a + b )( a – b ) = a² – b²

= ( x + 2i )( x – 2i )

= ( x )² – ( 2i )²

= x² – 4i²

= x² + 4

hope this helps

Bye !!

• ( x + 2 i ) ( x – 2 i ) = x ² – 4 i ² = x ² + 4

• (x + 2i)(x – 2i)

= x(x) – x(2i) + 2i(x) – 2i(2i)

= x^2 – 2ix + 2ix – 4i^2

= x^2 – 4(-1)

= x^2 – (-4)

= x^2 + 4