Problem 99 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

Multiplying the binomials \((x + 3)(x + 2)\) using the FOIL method results in \(x^2 + 5x + 6\).

Step 1: Identify the Method

The FOIL method stands for: First (multiply the first term in each binomial), Outer (multiply the outer term in the product), Inner (multiply the inner term), and Last (multiply the last term in each binomial). In the expression \((a + b)(c + d)\), using the FOIL method would look like this: \((a*c) + (a*d) + (b*c) + (b*d)\). Let's apply this to a concrete example.

Step 2: Applying the Method - First

Consider the example \((x + 3)(x + 2)\). The first terms of each binomial are 'x' and 'x'. Multiply these together to get \(x*x\) or \(x^2\).

Step 3: Applying the Method - Outer

Next, focus on the outer terms. These are 'x' from the first binomial and '2' in the second. Their product will be \(x*2\) or \(2x\).

Step 4: Applying the Method - Inner

Now look to the inner terms, which are '3' from the first binomial and 'x' from the second. Their product will be \(3*x\) or \(3x\).

Step 5: Applying the Method - Last

Lastly, focus on the last terms: '3' from the first binomial and '2' from the second. Their product is \(3*2\) or \(6\).

Step 6: Summing the Terms

The final step is to sum the results of each product in order. This results in the equation: \(x^2 + 2x + 3x + 6\). Combining like terms gives the final answer: \(x^2 + 5x + 6\).