Find each product. (x+7y)(3x-5y)

Key Concepts

Distributive Property

The distributive property states that a(b + c) = ab + ac. This principle 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.

Binomials

A binomial is a polynomial that contains exactly two terms, which can be separated by a plus or minus sign. In the expression (x + 7y)(3x - 5y), both (x + 7y) and (3x - 5y) are binomials. Understanding how to manipulate binomials is essential for performing operations like multiplication.

Combining Like Terms

Combining like terms involves 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 need to be combined to achieve the final simplified form.