Problem 20 - College Algebra

Question

Find each product. $$(x-5)(x+3)$$

Step-by-Step Solution

Answer

\(x^2 - 2x - 15\)

Step 1: Apply FOIL Method - First

Multiply the first terms from each binomial. In this case, the first term \(x\) in the first binomial should be multiplied with the first term \(x\) in the second binomial, yielding \(x^2\).

Step 2: Apply FOIL Method - Outer

Multiply the outer terms from each binomial. The outer terms are the first term from the first binomial and the second term from the second binomial, so \(x\) from the first binomial should be multiplied with \(3\) from the second binomial, yielding \(3x\).

Step 3: Apply FOIL Method - Inner

Next, multiply the inner terms from each binomial. The inner terms are the second term from the first binomial and the first term from the second binomial, so \(-5\) from the first binomial should be multiplied with \(x\) from the second binomial, yielding \(-5x\).

Step 4: Apply FOIL Method - Last

Finally, the last terms from each binomial are multiplied together. The last terms are the second terms in each binomial, so \(-5\) from the first binomial and \(3\) from the second binomial are multiplied together to give \(-15\).

Step 5: Simplify

Combine any like terms from the previous steps. The middle terms \(3x\) and \(-5x\) combine to give \(-2x\). So, the full simplified expression is \(x^2 - 2x - 15\).