Problem 22 - College Algebra

Question

Find each product. $$(x-1)(x+2)$$

Step-by-Step Solution

Answer

The product of \((x-1)\) and \((x+2)\) is \(x^2 + x - 2\).

Step 1: Apply FOIL Method - First Terms

Multiply the first terms of both binomials. In our case, that would be \(x\) from \(x - 1\) and \(x\) from \(x + 2\). The result is \(x * x = x^2\).

Step 2: Apply FOIL Method - Outer Terms

Multiply the outer terms of the binomials. Here, that's \(x\) from \(x - 1\) and \(2\) from \(x + 2\). So, \(x * 2 = 2x\).

Step 3: Apply FOIL Method - Inner Terms

Multiply the inner terms now. That gives us \(-1\) from \(x - 1\) and \(x\) from \(x + 2\). So, \(-1 * x = -x\).

Step 4: Apply FOIL Method - Last Terms

Lastly, multiply the last terms of the binomials. This gives us \(-1\) from \(x - 1\) and \(2\) from \(x + 2\). So, \(-1 * 2 = -2\).

Step 5: Combine Like Terms

Combine all the results from previous steps to form a new expression which is \(x^2 + 2x - x - 2\). Upon combining similar terms \(2x\) and \(-x\) , we get \(x^2 + x - 2\).