Problem 76 - Algebra 1: Concepts and Skills

Question

Find the product. $$(x-2)(x+11)$$

Step-by-Step Solution

Answer

The product of \( (x-2)(x+11) \) is \( x^2 + 9x - 22 \).

Step 1: Use the FOIL Method

The FOIL method stages for First, Outer, Inner and Last. To use FOIL, the first terms in each binomial are multiplied together, then the outer terms, the inner terms and finally the last terms.

Step 2: Multiply the first terms

The first term in each binomial is \(x\). When these are multiplied together, the product is \(x^2\).

Step 3: Multiply the outer terms

The outer terms are \(x\) and \(11\). When multiplied together, the product is \(11x\).

Step 4: Multiply the inner terms

The inner terms are \(-2\) and \(x\). When multiplied together, the product is \(-2x\).

Step 5: Multiply the last terms

The last terms are \(-2\) and \(11\), and their product is \(-22\).

Step 6: Combine like terms and write the final answer

Adding together the obtained products, we have \(x^2 + 11x - 2x -22\). By combining like terms, we arrive at the final expression \(x^2 + 9x - 22\).