In Exercises 15–58, find each product. (2x−5)(7x+2)

Verified step by step guidance

1. Identify the expression to be multiplied: $(2x-5)(7x+2)$.
2. Apply the distributive property (also known as the FOIL method for binomials): First, multiply the first terms: $2x\cdot 7x$.
3. Next, multiply the outer terms: $2x\cdot 2$.
4. Then, multiply the inner terms: $-5\cdot 7x$.
5. Finally, multiply the last terms: $-5\cdot 2$.

Key Concepts

Distributive Property

The Distributive Property states that a(b + c) = ab + ac. This property allows us to multiply a single term by two or more terms inside parentheses. In the context of the given expression, it will be used to distribute each term in the first binomial (2x - 5) across each term in the second binomial (7x + 2).

Binomial Multiplication

Binomial multiplication involves multiplying two binomials, which are algebraic expressions containing two terms. The result of multiplying two binomials is typically a polynomial with four terms, which can often be simplified. In this case, we will multiply (2x - 5) by (7x + 2) to find the product.

Combining Like Terms

Combining like terms is the process of simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. After using the Distributive Property to expand the product of the binomials, we will need to combine any like terms to express the final answer in its simplest form.