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Chapter 0: Problem 23

Find each product. $$(3 x+5)(2 x+1)$$

Short Answer

Expert verified
The product of the given binomials, \((3x+5)(2x+1)\), is \(6x^2 + 13x + 5\).

Step by step solution

01

Distribute the Terms:

Distribute each term in the first binomial across the terms in the second binomial. This gives us: \(3x \cdot 2x + 3x \cdot 1 + 5 \cdot 2x + 5 \cdot 1\).
02

Perform the Multiplication:

Now we perform the multiplication in each term which gives us: \(6x^2 + 3x + 10x + 5\).
03

Combine Like Terms:

The next step is to combine the like terms within the expression, which results in: \(6x^2 + 13x + 5\).

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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. \(\sqrt{7}+\sqrt{18} \square \sqrt{7+18}\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I subtracted \(\frac{3 x-5}{x-1}\) from \(\frac{x-3}{x-1}\) and obtained a constant.

What is a linear equation in one variable? Give an example of this type of equation.

Rationalize the numerator. $$\frac{\sqrt{x}+\sqrt{y}}{x^{2}-y^{2}}$$

Explain why \(|x|<-4\) has no solution.
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