Problem 99 - College Algebra

Question

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

Step-by-Step Solution

Answer

The product of the multiplication of two binomials \( (a + b) \) and \( (c + d) \) using the FOIL method is \( (a*c) + (a*d) + (b*c) + (b*d) \)

Step 1: Define the Two Binomials

Consider Product of two binomials, say \( (a + b) (c + d) \)

Step 2: Apply FOIL Method

FOIL stands for First, Outside, Inside, Last. Multiply the First terms in each binomial, then the Outside terms, the Inside terms, and finally the Last terms. In our example: The first terms are a and c, the outside terms are a and d, the inside terms are b and c, and the last term are b and d.

Step 3: Multiply and Simplify

Multiply these term pairs to get: \((a*c) + (a*d) + (b*c) + (b*d)\), which is the result of the multiplication of the two binomials