Multiplying monomials/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., 3x^2, -5, 7y).

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^3 + 3x^2 - x + 5).

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 combine like terms if necessary.

Tags

CCSS.HSA.APR.A.1

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 inside a parenthesis.

Tags

CCSS.6.EE.A.3

Front

Multiply: -2x^2(-6x + 5)

Back

12x^3 - 10x^2.

Tags

CCSS.HSA.APR.A.1

Front

Multiply: 5x(4x^3 + 8)

Back

20x^4 + 40x.

Tags

CCSS.HSA.APR.A.1

Front

Multiply: 3a(5a^2 + 8a + 2)

Back

15a^3 + 24a^2 + 6a.

Tags

CCSS.HSA.APR.A.1

Front

Multiply: 7y(5y^2 + 2y + 3)

Back

35y^3 + 14y^2 + 21y.

Tags

CCSS.HSA.APR.A.1

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power, which can be combined by adding or subtracting their coefficients (e.g., 3x^2 and 5x^2 are like terms).

Tags

CCSS.6.EE.A.2B

Front

What is the degree of a polynomial?

Back

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