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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, 3, x and minus, 5, y, squared are both monomials.

What is a binomial?

A binomial is an algebraic expression that has two terms. For example, 2, x, plus, 1 and minus, 4, y, squared, plus, 3, y 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, squared, plus, 3, x, plus, 1 and minus, 5, y, cubed, plus, 2, y, squared, minus, 6, y, plus, 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.

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 left parenthesis, a, plus, b, right parenthesis, squared, equals, a, squared, plus, 2, a, b, plus, b, squared. Another special product is the difference of squares: left parenthesis, a, plus, b, right parenthesis, left parenthesis, a, minus, b, right parenthesis, equals, a, squared, minus, b, squared.

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, squared, plus, 8, x into 2, x, left parenthesis, 3, x, plus, 4, right parenthesis.

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.

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