Combining the Rules
Here are a few more examples where you use a combination of the rules from the previous pages.
Example 1
Expand
Here, you have two options. The first is to multiply the two parentheses, and then multiply each term in the resulting expression with 2. The other is to first multiply each term in the first pair of parentheses with 2, and then multiply the resulting expression with the other pair of parentheses. I’ll show you both, the first method first:
Example 2
Expand the expression
Remember that is the same as , and that
because it doesn’t matter which side of the parentheses the number is. That gives you
Next, you’ll look at an example where you multiply three pairs of parentheses. The same rules that applied earlier are still in effect. You begin by multiplying two of the parentheses, and then you multiply that product with the third pair of parentheses.
Example 3
Expand the expression .
First, you multiply the first two parentheses, and then you multiply that product with the third pair of parentheses:
To finish off you’ll look at an example with powers and parentheses.
Example 4
Expand the expression
You should start with the products. Expand and individually:
and