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### Course: Algebra 1 > Unit 13

Lesson 9: Strategy in factoring quadratics# Quadratics: Multiplying & factoring: FAQ

Frequently asked questions about multiplying & factoring quadratics

## What is a monomial?

A monomial is an algebraic expression that has just one term. For example, $3x$ and $-5{y}^{2}$ are both monomials.

## What is a binomial?

A binomial is an algebraic expression that has two terms. For example, $2x+1$ and $-4{y}^{2}+3y$ are both binomials.

## What is a polynomial?

A polynomial is an algebraic expression made up of one or more terms. Monomials and binomials are both types of polynomials. Other examples include $2{x}^{2}+3x+1$ and $-5{y}^{3}+2{y}^{2}-6y+8$ .

Practice with our Polynomials intro exercise.

## What is an area model?

An area model is a way of visually representing multiplication. We divide a shape (usually a square or a rectangle) into sections to show the different factors involved in the multiplication.

Practice with our Multiply monomials by polynomials (basic): area model exercise.

Practice with our Multiply binomials: area model exercise.

## What are special products of binomials?

There are a few patterns that we can use to quickly multiply certain types of binomials. For example, when we square a binomial (multiply it by itself), we can use the formula $(a+b{)}^{2}={a}^{2}+2ab+{b}^{2}$ . Another special product is the difference of squares: $(a+b)(a-b)={a}^{2}-{b}^{2}$ .

Practice with our Multiply perfect squares of binomials
exercise.

Practice with our Multiply difference of squares exercise.

## What does it mean to factor an expression?

Factoring an expression means breaking it down into simpler parts that we can multiply together to get the original expression. For example, we can factor $6{x}^{2}+8x$ into $2x(3x+4)$ .

Practice with our GCF factoring introduction exercise.

## Where can we use all of this?

Understanding how to multiply and factor quadratics has many applications in the real world. For example, we can use these skills to solve quadratic equations, which come up in physics, engineering, and business.

## Want to join the conversation?

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