Find each product. See Example 5. (3x + 1) (2x - 7)

Key Concepts

Distributive Property

The distributive property is a fundamental algebraic principle that states a(b + c) = ab + ac. It 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 across each term in the second binomial.

Binomial Multiplication

Binomial multiplication involves multiplying two binomials, which are algebraic expressions containing two terms. The result is typically a polynomial of degree equal to the sum of the degrees of the binomials. In this case, (3x + 1)(2x - 7) will yield a polynomial that combines the products of each term from both binomials.

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 applying the distributive property to the product of the binomials, the resulting expression may contain like terms that can be combined to produce a simpler form, making the final answer clearer.