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Chapter 5: Problem 55

Find each product. In each case, neither factor is a monomial. $$(x+3)(x+5)$$

Short Answer

Expert verified
The product of the binomials \( (x + 3)(x + 5) \) is \( x^2 + 8x + 15 \).

Step by step solution

01

Apply Distributive Property (FOIL)

Apply the distributive property which is also known as FOIL - First, Outer, Inner, Last. Here, the first terms are \(x * x\), the outer terms are \(x * 5\), the inner terms are \(3 * x\) and the last terms are \(3 * 5\).
02

Calculate Products

Calculate the products for each term: \(x * x = x^2\), \(x * 5 = 5x\), \(3 * x = 3x\) and \(3 * 5 = 15\).
03

Sum the Products

Sum the products from the previous step: \(x^2 + 5x + 3x + 15\).
04

Simplify the Expression

Combine like terms to simplify the expression. The terms \(5x\) and \(3x\) are alike and will be added together to yield \(8x\), yielding \(x^2 + 8x + 15\) as the final expression.

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