Problem 23 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: Multiply the First Terms

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

Step 2: Multiply the Outer Terms

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

Step 3: Multiply the Inner Terms

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

Step 4: Multiply the Last Terms

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

Step 5: Add the Results

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