Problem 45 - College Algebra Essentials

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: Identify the binomial

The given problem consists of binomial \((x-3)\) to the power of 2. It means \((x-3)^{2} = (x-3) * (x-3)\)

Step 2: Perform the binomial expansion

Apply the algebraic rule for squaring a binomial difference: \((a-b)^{2} = a^{2} - 2ab + b^{2}\), where a = x and b = 3. This gives us \(x^{2} - 2*3*x + 3^{2}\)

Step 3: Simplify the expression

Now, compute for the multiples and add them up. This gives us \(x^{2} - 6x + 9\)