Multiplying Monomials and Polynomials

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., 5x, -3, 4xy).

Front

What is a polynomial?

Back

A polynomial is an expression that consists of variables raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication (e.g., 2x^2 + 3x + 1).

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 (e.g., 3x(2x + 4) = 6x^2 + 12x).

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 sum.

Front

Simplify: 10x(x + 2)

Back

10x^2 + 20x.

Front

Simplify: 4m(3m^7 + 2m^5)

Back

12m^8 + 8m^6.

Front

Simplify: 5(3x + 2)

Back

15x + 10.

Front

Simplify: 3x^3(2x^2 + 9x + 6)

Back

6x^5 + 27x^4 + 18x^3.

Front

Simplify: 6v(2v + 3)

Back

12v^2 + 18v.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression (e.g., in 4x^3 + 2x^2, the degree is 3).