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Chapter 0: Problem 53

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

Short Answer

Expert verified
The product of \((2x + 3)^3\) is \(8x^3 + 36x^2 + 54x + 27\).

Step by step solution

01

Identify the terms

In order to solve the problem, first recognize the two terms in the binomial, \(a\) and \(b\). In this case, \(a = 2x\) and \(b = 3\).
02

Use the cube of a binomial formula

The general formula for the cube of a binomial \((a+b)^3\) is \(a^3 + 3a^2b + 3ab^2 + b^3\). Replace \(a\) and \(b\) in the formula with the identified terms. This results in the expression: \((2x)^3 + 3(2x)^2*3 + 3*2x*(3)^2 + (3)^3\).
03

Simplify the expression

To simplify the expression, perform operations as indicated. This results in the final solution: \(8x^3 + 36x^2 + 54x + 27\).

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Most popular questions from this chapter

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

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. Parts for an automobile repair cost \(\$ 175 .\) The mechanic charges \(\$ 34\) per hour. If you receive an estimate for at least \(\$ 226\) and at most \(\$ 294\) for fixing the car. what is the time interval that the mechanic will be working on the job?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \((2 x-3)^{2}=25\) is equivalent to \(2 x-3=5\).

Perform the indicated operations. $$(x-y)^{-1}+(x-y)^{-2}$$

Describe ways in which solving a linear inequality is similar to solving a linear equation.
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