Problem 45 - College Algebra

Question

Find each product. $$(x-3)^{2}$$

Step-by-Step Solution

Answer

The product of \((x-3)^{2}\) is \(x^{2} - 6x + 9\).

Step 1: Understand the Binomial Squared

A binomial squared \((x-a)^{2}\) can be rewritten as \((x - a)(x - a)\). We can apply this to our case, and rewrite \((x-3)^{2}\) as \((x - 3)(x - 3)\).

Step 2: Using the FOIL Method

Next, apply the First, Outside, Inside, Last (FOIL) method to multiplied the expanded binomials. This means multiplying the first terms together, then the two terms on the outside, then the two terms on the inside, and finally the last two terms. So it becomes \(x * x - 3 * x - 3 * x + 3 * 3\).

Step 3: Simplify the Result

Now simplify the resulting expression. The obtained result \(x * x - 3 * x - 3 * x + 3 * 3\) simplifies to \(x^{2} - 6x + 9\).