Problem 19 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The product of the binomials \((x + 7)(x + 3)\) is \( x^2 + 10x + 21 \).

Step 1: Apply the FOIL Method - First

First, multiply the first terms in each binomial together. In this case, it would be \( x \) times \( x \) which equals \( x^2 \).

Step 2: Apply the FOIL Method - Outer

Next, multiply the outer terms together. That would be \( x \) times \( 3 \) which equals \( 3x \).

Step 3: Apply the FOIL Method - Inner

Then, multiply the inner terms together. This would be \( 7 \) times \( x \) which equals \( 7x \).

Step 4: Apply the FOIL Method - Last

Lastly, multiply the last terms in each binomial together. So, \( 7 \) times \( 3 \) equals \( 21 \).

Step 5: Combine Like Terms

Combine the like terms we got from the previous steps i.e., \( 3x \) and \( 7x \). So, \( 3x + 7x = 10x \). Our equation now looks like this: \( x^2 + 10x + 21 \).