 Review of Distributive Rule and FOIL with Integers
 Multiplying Radical Expressions using Distribution and FOIL
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. For example:


Distribute 2 into 4 and 3



Multiply inside the parentheses



Add 8 to 6



Our Solution

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


Apply steps to FOIL



Add and subtract



Our Solution

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.


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:


Apply the steps to FOIL



simplifies to the integer 3



Combine like terms



Our Solution


 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.


 FOIL
 An acronym to remember the steps for distributing factors in binomial multiplication: first, outside, inside, last.
A review of the distributive property and FOIL allows us to distribute outside factors into all terms of another factor. A helpful hint when multiplying radical expressions using distribution and FOIL is to remember that multiplying 2 square root terms together will cancel out the square root operation. For example, the square root of 8 times the square root of 8 is just 8.