Exercises 73–75 will help you prepare for the material covered in the next section. Multiply: (7 - 3x)(- 2 - 5x)

Key Concepts

Distributive Property

The distributive property states that a(b + c) = ab + ac. This principle allows us to multiply a single term by each term within a parenthesis. In the context of the given expression, it will be essential to apply this property to multiply each term in the first binomial by each term in the second binomial.

Binomial Multiplication

Binomial multiplication involves multiplying two binomials, which are algebraic expressions containing two terms. The result of multiplying two binomials is a polynomial, typically a trinomial. Understanding how to combine like terms after applying the distributive property is crucial for simplifying the resulting expression.

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 multiplying the binomials, the resulting polynomial may contain terms that can be combined to produce a simpler expression. This step is vital for arriving at the final answer.