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 (e.g., 3x, -5, 7xy).

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 (e.g., 2x^2 + 3x - 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 simplify the result.

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

Back

-10x^3 - 16x

Front

Multiply: -8x(x - 8)

Back

-8x^2 + 64x

Front

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

Back

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

Front

What is the result of subtracting polynomials?

Back

Subtracting polynomials involves subtracting the coefficients of like terms from each other.

Front

Subtract: (k^2 + 8k + 1) - (3k^2 + 5k + 8)

Back

-2k^2 + 3k - 7

Front

What is the result of adding polynomials?

Back

Adding polynomials involves adding the coefficients of like terms together.