Problem 93 - College Algebra

Question

Explain how to multiply two binomials using the FOIL method. Give an example with your explanation.

Step-by-Step Solution

Answer

To utilize the FOIL method, first, treat each binomial as a separate entity and multiply the first terms of each, then the outer terms, followed by the inner terms, and finally, the last terms. Addition of these four products yields the final result. For the binomials \( (a+b) \) and \( (x+y) \), the answer using the FOIL method will be \( ax + ay + bx + by \).

Step 1: Introduction of the binomials

Let's take two binomials as \( (a+b) \) and \( (x+y) \). We have to multiply these binomials using the FOIL method.

Step 2: Applying the 'First' Step

First means we multiply the first terms in each binomial. Here it would be \( a \) and \( x \), yielding \( a*x \) as the first term of our result.

Step 3: Applying the 'Outer' and 'Inner' Steps

Outer means we multiply the outside terms in the product, which are \( a \) and \( y \). Inner means we multiply the inside terms, \( b \) and \( x \). These yield \( a*y \) and \( b*x \) respectively.

Step 4: Applying the 'Last' Step

Last means we multiply the last terms in each binomial, which are \( b \) and \( y \), to yield \( b*y \).

Step 5: Combining the Results

Combine all obtained terms together in an algebraic expression, which is the end result of the FOIL method. This gives us the expression \( ax + ay + bx + by \).