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Chapter 0: Problem 43

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

Short Answer

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

Step by step solution

01

Identify variables in the formula

In the given formula, identify \(a\) and \(b\). In this case, \(a = 2x\) and \(b = 3\).
02

Apply the binomial theorem

Now apply the binomial theorem, \( (a + b)^2 = a^2 + 2ab + b^2 \) by substituting the values identified in step 1. This results in: \( (2x)^2 + 2*2x*3 + 3^2 \).
03

Simplify the equation

Simplify the equation by multiplying and adding where necessary, resulting in: \(4x^2 + 12x + 9\)

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Most popular questions from this chapter

Place the correct symbol, \(>\) or \(<\), in the shaded area between the given numbers. Do not use a calculator. Then check your result with a calculator. \(a, 3^{\frac{1}{2}}\square 3^{1}\) b. \(\sqrt{7}+\sqrt{18} \square \sqrt{7+18}\)

Explain how to add rational expressions having no common factors in their denominators. Use \(\frac{3}{x+5}+\frac{7}{x+2}\) in your explanation.

Explain how to determine which numbers must be excluded from the domain of a rational expression.

$$\begin{array}{l} \text { Find the exact value of } \sqrt{13+\sqrt{2}+\frac{7}{3+\sqrt{2}}} \text { without } \\ \text { the use of a calculator. } \end{array}$$

Describe the solution set of \(|x|>-4\)
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