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Chapter 0: Problem 43

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

Short Answer

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

Step by step solution

01

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 \((2x + 3) * (2x + 3)\).
02

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 \(Last: 3 * 3 = 9\).
03

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 \(4x^2 + 12x + 9\).

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Most popular questions from this chapter

$$\text { Factor completely.}$$ $$2 x^{2}-7 x y^{2}+3 y^{4}$$

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