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Chapter 5: Problem 26

Multiply the monomials. $$(8 x)(3 x)$$

Short Answer

Expert verified
The product of the two monomials \(8x\) and \(3x\) is \(24x^2\).

Step by step solution

01

Multiply the Coefficients

Start by multiplying the coefficients (the numbers) together. In this case, those are 8 and 3, which when multiplied give 24.
02

Multiply the Variables

Next, multiply the variables. When you multiply variables with the same base, you add their powers. In this case both variables are \(x\) with power 1 (since no power is indicated, it is understood to be 1). Therefore, when you multiply \(x\) by \(x\), you add the powers to get \(x^2\).
03

Combine the Product of Coefficients and Variables

Finally, combine the product of the coefficients and the product of the variables to get the answer. So, 24 (the product of the coefficients) times \(x^2\) (the product of the variables) equals \(24x^2\).

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Most popular questions from this chapter

Make Sense? In Exercises \(96-99\), determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I divide monomials by dividing coefficients and subtracting exponents.

In each exercise, find the product. $$4 x^{3}\left(4 x^{2}-3 x+1\right)$$

Explain how to multiply polynomials when neither is a monomial. Give an example.

Use a vertical format to find each product. $$\begin{array}{r}7 x^{3}-5 x^{2}+6 x \\\3 x^{2}-4 x \\\\\hline\end{array}$$

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)^{2}\) b. \((x+5)^{2}\)
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