Skill: Multiply two binomials

Explanation and Free Practice Resources

Multiplying two binomials involves applying the distributive property so that each term in one binomial multiplies each term in the other, then combining like terms and correctly managing coefficients, variables, and signs. An area model or symbolic expansion reveals why products such as $(ax+b)(cx+d)$ produce a quadratic expression and supports later work with polynomial simplification, expansion, and factoring; this scope focuses on one-variable binomials with numerical coefficients, not multivariable or abstract polynomial generalizations.

On this page:

Learn “Multiply two binomials” with a detailed explanation of the concept
Master “Multiply two binomials” with unlimited, free practice problems
Download (or modify) a free worksheet on Multiply two binomials you can use at home or in class with practice problems that scaffold and explore “Multiply two binomials” from different perspectives.
Start working on adaptive units like “Polynomials and Quadratics - Intro” or “Algebra Basic Concepts - Advanced” that introduce, teach, or practice “Multiply two binomials” to maximize your learning.

Detailed Explanation: Multiply two binomials

To multiply two binomials, use the distributive property: multiply each term in the first binomial by each term in the second binomial. Then combine like terms.

Example:

(2x+3)(x-4)

Multiply each term in the first binomial by both terms in the second:

(2x)(x)+(2x)(-4)+3(x)+3(-4)

Now simplify each product:

2x^2-8x+3x-12

Combine the like terms $-8x$ and $3x$ :

-8x+3x=-5x

Therefore,

\boxed{(2x+3)(x-4)=2x^2-5x-12}

Check that there are four products before combining like terms: $2x\cdot x$ , $2x\cdot(-4)$ , $3\cdot x$ , and $3\cdot(-4)$ .

Learn by doing: Multiply two binomials

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Your results

Practice with unlimited practice problems

Algebraic Functions - Multiply Bracketed Terms, Same Variable (First Term)

Earned ?

Download/Modify Free Grade 10 'Multiply two binomials' Worksheet

Print this free 'Multiply two binomials' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.

Units Teaching This Skill

These adaptive units introduce, teach, or reinforce this skill (Multiply two binomials) through scaffolded problems that grow in difficulty as concepts are understood.