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Chapter 0: Problem 23

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

Short Answer

Expert verified
The product of \(3x + 5\) and \(2x + 1\) is \(6x^2 + 13x + 5\).

Step by step solution

01

Multiply the First Terms

First multiply the first terms in each binomial. In this case that would be \(3x\) and \(2x\), which results in \(6x^2\).
02

Multiply the Outer Terms

Next, multiply the outer terms, which are \(3x\) in the first binomial and \(1\) in the second. This gives \(3x\).
03

Multiply the Inner Terms

Then, multiply the inner terms, which are \(5\) in the first binomial and \(2x\) in the second. This gives \(10x\).
04

Multiply the Last Terms

Now, multiply the last terms, which are \(5\) in the first binomial and \(1\) in the second. This gives \(5\).
05

Add the Results

Finally, add the results of the previous steps together. Therefore, \(6x^2 + 3x + 10x + 5\) simplifies to \(6x^2 + 13x + 5\).

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