Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x + 5 is a polynomial.

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. It allows you to multiply a single term by each term in a polynomial.

Front

How do you multiply a binomial by a trinomial?

Back

To multiply a binomial by a trinomial, distribute each term in the binomial to each term in the trinomial, then combine like terms.

Front

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

Back

The result is x^2 + 5x + 6.

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)^2 is equal to a^2 + 2ab + b^2.

Front

What is the product of (5s + 2)^2?

Back

The product is 25s^2 + 20s + 4.

Front

What is the result of multiplying (5x + 2y)(x^2 - 3xy + 6)?

Back

The result is 5x^3 - 13x^2y - 6xy^2 - 30x + 12y^2.

Front

What is the result of (x - 3)(x^2 + 2x + 7)?

Back

The result is x^3 - x^2 + x - 21.

Front

What does it mean to simplify an expression?

Back

Simplifying an expression means to reduce it to its simplest form, combining like terms and eliminating unnecessary parentheses.