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.

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.

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.

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

What is the result of multiplying 10x by (2x^2 + 3x + 4)?

Back

The result is 20x^3 + 30x^2 + 40x.

Front

How do you simplify the expression -3x^2(7x^2 - x + 4)?

Back

Distribute -3x^2 to each term: -3x^2 * 7x^2 = -21x^4, -3x^2 * -x = 3x^3, -3x^2 * 4 = -12x^2, resulting in -21x^4 + 3x^3 - 12x^2.

Front

What is the result of multiplying 10 by (x + y + z)?

Back

The result is 10x + 10y + 10z.

Front

How do you multiply two binomials?

Back

Use the distributive property (FOIL method): First, Outer, Inner, Last terms.

Front

What is the result of multiplying 5x by (5x + 5)?

Back

The result is 25x^2 + 25x.

Front

How do you simplify the expression 10(x - 2)?

Back

Distribute 10 to both terms: 10 * x - 10 * 2 = 10x - 20.