Problem 43 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The product of squaring the binomial \(2x+3\) is \(4x^2 + 12x + 9\).

Step 1: Write Down the Binomial Squared

Given the problem, the first step is to write down the binomial squared: \((2x + 3)^2\). This is the same as saying \((2x + 3) * (2x + 3)\).

Step 2: Apply the FOIL Method

To square a binomial, we must apply the FOIL (First, Outer, Inner, Last) method. This entails multiplying the first terms of both binomials together, then the outer terms, inner terms, and finally the last terms. For our problem, this looks like the following: \(First: 2x * 2x = 4x^2\), \(Outer: 2x * 3 = 6x\), \(Inner: 3*2x = 6x\), and \(Last: 3 * 3 = 9\).

Step 3: Combine Like Terms

After applying the FOIL method, we have four terms: \(4x^2, 6x, 6x, 9\). We must now combine the like terms (the terms with the same variable and exponent), which in this case is \(6x\) and \(6x\) to simplify the expression. This gives us \(4x^2 + 12x + 9\).