Problem 22 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: Apply the distributive property

The first step is to apply the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Start by multiplying the first terms in each binomial together, then the outer terms, followed by the inner terms and finally the last terms. So for the expression \((x-1)(x+2)\), Start by multiplying \(x\) (from the \(x-1)\) by \(x\) (from the \(x+2)\), giving \(x^2\).

Step 2: Multiply the outer terms

Next, multiply the outer terms together. In this case, that's \(x\) (from the \(x-1)\) and \(2\) (from the \(x+2)\). This gives \(2x\).

Step 3: Multiply the inner terms

Now, multiply the inner terms, that's \(-1\) (from the \(x-1)\) and \(x\) (from the \(x+2)\) together. This gives \(-x\).

Step 4: Multiply the last terms

Multiply the last terms together. So, \(-1\) (from the \(x-1)\) and \(2\) (from the \(x+2)\). Thus, it gives \(-2\).

Step 5: Combine like terms

In the final stage, you combine all the terms from the previous steps. In this case, that's \(x^2\), \(2x\), \(-x\), and \(-2\). Combine the \(2x\) and \(-x\), resulting in \(x\).