Multiplying Monomials and Binomials (Boyer)

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, which can be a constant, a variable, or a product of constants and variables (e.g., 3x^2, -5, 7y).

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, which can be separated by a plus or minus sign (e.g., x + 2, 3x^2 - 4).

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term in a binomial.

Front

How do you multiply a monomial by a binomial?

Back

Use the Distributive Property: Multiply the monomial by each term in the binomial and combine like terms.

Front

What is the result of multiplying x^3(2x^2 + 3x)?

Back

2x^5 + 3x^4.

Front

How do you simplify 5(3x + 2)?

Back

Distribute 5 to both terms: 15x + 10.

Front

What is the product of (4x + 1)(5x - 2)?

Back

20x^2 - 3x - 2.

Front

How do you multiply two binomials?

Back

Use the FOIL method: First, Outside, Inside, Last to find the product.

Front

What is the result of multiplying -3x^2(7x^2 - x + 4)?

Back

-21x^4 + 3x^3 - 12x^2.

Front

What is the product of (3x - 6)(7x + 7)?

Back

21x^2 - 21x - 42.