Multiply each of the following expressions.

1. $(x + i)(x - i)$ 

   Step 1 (a):

   Sketch and label a square with four interior squares like the one at right.

   Step 2 (a):

   Multiply each term together.
   Do you see a way you can simplify them more?

   Answer (a):

   $x^2 + 1$

   	$x-i$
   $x$ $+$ $i$

   	$x-i$
   $x$ $+$ $i$	$x^2$	$-xi$
   	$xi$	$-i^2$

2. $(x + 2i)(x - 2i)$ 

   Hint (b):

   See steps for part (a).

3. Write the expression $x^2 + 25$ as a product.

   Hint (c):

   Reverse what you did in parts (a) and (b).