Multiplying Polynomials

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

What does it mean to multiply polynomials?

Back

Multiplying polynomials involves using the distributive property to combine each term in one polynomial with each term in another polynomial.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

How do you simplify the expression 5(3x + 2)?

Back

To simplify 5(3x + 2), apply the distributive property: 5 * 3x + 5 * 2 = 15x + 10.

Front

What is the result of multiplying (x + 7)(x + 9)?

Back

The result is x^2 + 16x + 63, obtained by applying the distributive property to each term.

Front

What is the result of simplifying 2x(-2x - 3)?

Back

The result is -4x^2 - 6x, achieved by distributing 2x to both terms inside the parentheses.

Front

What is the product of (x + 2)(x + 3)?

Back

The product is x^2 + 5x + 6, found by multiplying each term in the first polynomial by each term in the second.

Front

How do you multiply the polynomials (2x - 1)(x + 2)?

Back

To multiply (2x - 1)(x + 2), distribute each term: 2x*x + 2*2x - 1*x - 1*2 = 2x^2 + 3x - 2.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as (x + 2) or (3x - 5).

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms, such as (x^2 + 5x + 6).