Multiplying Polynomials by Monomials

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.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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.

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

Multiply: 10x(2x^2 + 3x + 4)

Back

20x^3 + 30x^2 + 40x

Front

Multiply: -8x(x - 8)

Back

-8x^2 + 64x

Front

Multiply: -6y(y^5 + 8y)

Back

-6y^6 - 48y^2

Front

Multiply: -2x(5x^2 + 8)

Back

-10x^3 - 16x

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial, representing how many times the variable is multiplied.

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.