Problem 19 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1 - First

Multiply the first terms in each binomial. The first terms are 'x' in both the binomials, hence the product will be \( x \cdot x = x^2 \)

Step 2 - Outer

Multiply the outer terms in the binomials. The outer terms are 'x' from the first binomial and '3' from the second binomial, hence the product will be \( x \cdot 3 = 3x \)

Step 3 - Inner

Multiply the inner terms in the binomials. The inner terms are '7' from the first binomial and 'x' from the second binomial, hence the product will be \( 7 \cdot x = 7x \)

Step 4 - Last

Multiply the last terms in each binomial. The last terms are '7' from the first and '3' from the second binomial, hence the product will be \( 7 \cdot 3 = 21 \)

Step 5 - Combine like terms

Now combine the products obtained from the outer and the inner steps (similar terms) to simplify the expression: \( x^2 + 3x + 7x + 21 \) which simplifies to \( x^2 + 10x + 21 \)