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Chapter 0: Problem 54

Find each product. $$(3 x+4)^{3}$$

Short Answer

Expert verified
The expanded form of the cubic binomial is \(27x^{3}+108x^{2}+192x+64\).

Step by step solution

01

Apply the Binomial Expansion formula

The cube of a binomial, (a+b)^3, can be expanded using the formula according to the binomial theorem. The formula is \(a^{3}+3a^{2}b+3ab^{2}+b^{3}\). Here, a=3x and b=4. Replace a and b in the formula with the values.
02

Calculate the value for each term

After replacing a and b into the formula, you get \((3x)^{3}+3(3x)^{2}(4)+3(3x)(4)^{2}+4^{3}\). Calculate each term separately.
03

Simplify the equation

After calculations, you will get 27x^{3}+108x^{2}+192x+64. Combine like terms, if any.

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Most popular questions from this chapter

In Exercises 132鈥�135, determine whether each statement makes sense or does not make sense, and explain your reasoning. There are many exponential expressions that are equal to \(36 x^{12},\) such as \(\left(6 x^{6}\right)^{2},\left(6 x^{3}\right)\left(6 x^{9}\right), 36\left(x^{3}\right)^{9},\) and \(6^{2}\left(x^{2}\right)^{6}\)

Simplify using properties of exponents. $$\frac{\left(3 y^{\frac{1}{4}}\right)^{3}}{y^{\frac{1}{12}}}$$

Find the exact value of \(\sqrt{13+\sqrt{2}+\frac{7}{3+\sqrt{2}}}\) without the use of a calculator.

Factor completely. $$ x^{2 n}+6 x^{n}+8 $$

In Exercises 132鈥�135, determine whether each statement makes sense or does not make sense, and explain your reasoning. If \(5^{-2}\) is raised to the third power, the result is a number between 0 and 1
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