Problem 24 - College Algebra

Question

Find each product. $$(7 x+4)(3 x+1)$$

Step-by-Step Solution

Answer

The product is \(21x^2+19x+4\)

Step 1: Distribute the terms in the first binomial

Multiply each term in the first binomial with each term in the second binomial. This provides \(7x*3x + 7x*1 + 4*3x + 4*1\)

Step 2: Simplification

Simplify the expressions obtained in Step 1. For term \(7x*3x\) we get \(21x^2\), for \(7x*1\) we get \(7x\), for \(4*3x\) we get \(12x\), and for \(4*1\) we get \(4\)

Step 3: Combine like terms

Combine similar terms in order to simplify the expression further. The term \(7x\) and \(12x\) are similar and can be added together to give \(19x\).

Step 4: Write the final expression

Write the result from step 3 into a single expression to get the final answer. Hence, \(21x^2+19x+4\).