Algebra - Lesson 8-2 - Multiplying Monomials and Polynomials

Front

What is a monomial?

Back

A monomial is an algebraic expression that consists of a single term, which can be a number, a variable, or a product of numbers and variables raised to non-negative integer powers.

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of two or more terms, which can include constants, variables, and non-negative integer exponents.

Front

How do you multiply a monomial by a polynomial?

Back

To multiply a monomial by a polynomial, distribute the monomial to each term of the polynomial and simplify.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

What does it mean to combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.

Front

What is the result of multiplying -3x²(7x² - x + 4)?

Back

-21x⁴ + 3x³ - 12x².

Front

What is the result of multiplying x³(2x² + 3x)?

Back

2x⁵ + 3x⁴.

Front

How do you find the sum of two polynomials?

Back

To find the sum of two polynomials, combine like terms from both polynomials.

Front

What is the result of (2x² + 5x - 7) + (3 - 4x² + 6x)?

Back

-2x² + 11x - 4.

Front

What is the result of (3x⁴ - 4 - 5x²) - (1 - x² + 2x³)?

Back

3x⁴ - 2x³ - 4x² - 5.