Multiplying Radical Expressions

1. Review of Distributive Rule and FOIL with Integers

The distributive rule allows us to distribute an outside factor into all terms of another factor.

EXAMPLE

	Distribute 2 into 4 and 3
	Multiply inside the parentheses
	Add 8 to 6
	Our Solution

If we have two factors in the form , we can use the distributive property in a different way, commonly referred to as the FOIL method.

EXAMPLE

	Apply steps to FOIL
	Add and subtract
	Our Solution

term to know

FOIL

An acronym to remember the steps for distributing factors in binomial multiplication: first, outside, inside, last.

2. Multiplying Radical Expressions using Distribution and FOIL

The distributive rule and FOIL method can be applied to multiply expressions with radicals as well. First, we will look at an example of distribution, where two identical radicals are multiplied together.

EXAMPLE

	Distribute the square root of 2
	simplifies to the integer 2
	Our Solution

We can also use the FOIL method to distribute across two binomials in multiplication when there are radicals. This is illustrated in the following example:

EXAMPLE

	Apply the steps to FOIL
	simplifies to the integer 3
	Combine like terms
	Our Solution

big idea

The distributive rule and the FOIL method can be applied to expressions containing radicals as well. When two identical square roots are multiplied by each other, it evaluates to the expression underneath the square root. This property also applies to other roots, such as cube roots, but the identical radical needs to be multiplied by itself 3 times, and so on.