Monomial times Polynomial (no simplifying)

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 raised to non-negative integer powers.

Front

What is a polynomial?

Back

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

Front

What does it mean to multiply a monomial by a polynomial?

Back

Multiplying a monomial by a polynomial involves distributing the monomial to each term of the polynomial.

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: 3x(5x^2 - 7x - 8)

Back

15x^3 - 21x^2 - 24x

Front

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

Back

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

Front

Simplify: -3x^2(7x^2 - x + 4)

Back

-21x^4 + 3x^3 - 12x^2

Front

What is the result of multiplying a negative monomial by a polynomial?

Back

The result will have the same degree as the polynomial, but the signs of the terms will be affected by the negative monomial.

Front

Simplify: -3x^2(7x^2 - x + 4)

Back

-21x^4 + 3x^3 - 12x^2

Front

Simplify: 10x(x + 2)

Back

10x^2 + 20x