Quadratics: Multiplying & factoring: FAQ

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

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

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

Practice with our Polynomials intro exercise.

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.

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 $(a+b)^2 = a^2 + 2ab + b^2$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: $(a+b)(a-b) = a^2 - b^2$left parenthesis, a, plus, b, right parenthesis, left parenthesis, a, minus, b, right parenthesis, equals, a, squared, minus, b, squared.

Practice with our Multiply perfect squares of binomials exercise.

Practice with our Multiply difference of squares exercise.

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 $6x^2 + 8x$6, x, squared, plus, 8, x into $2x(3x+4)$2, x, left parenthesis, 3, x, plus, 4, right parenthesis.

Practice with our GCF factoring introduction exercise.

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.