These worksheets will help your students learn how to identify and multiply monomials and binomials.

A math term is a combination of numbers and variables. A binomial is an expression that consists of two different terms. Your students will use this collection of activity sheets to practice multiplying algebraic expressions using monomials and binomials. The full set of worksheets introduces your students to the concept of binomial multiplication, and provides examples, short practice sets, longer sets of questions, and review quizzes. Binary multiplication is relatively simple, in the grand scheme of things. They are products that involve using only two forms of integers (ones and zeroes). Use these worksheets to learn and practice solving binomial product equations.

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Multiply Binomials by Monomials Lesson

Multiply Binomials by Monomials Lesson

We start with a foundational level problem for you and this lesson walks you through solving it. Learn how to solve binomial equations such as "x(x + 7)"

Try the Skill Worksheet

Try the Skill

Get more practice using the method we just outlined for you. Example: (y - 2)(y - 9)

Practice Worksheet

Practice Worksheet

Practice the method we have discussed by working with 10 different problems that have you multiply binomial equations. Example: (2y + 5) (y + 6)

Binomial Multiplication Skills Worksheet

Binomial Multiplication Skills

Approach these problems using what you have learned so far. An example of this type of problem would be: (y - 5) (-3)

Boxed Out Worksheet

Boxed Out Worksheet

We give you plenty of room to spread out your work here. Do not let the negative symbols throw you off course. Just take them in strid and remember your properties of integers. Example: -11y(y + 1)

Warm Up Worksheet

Warm Up

A great way to review this as a an entire class. You can break into several steps for students. Example: 10(y - 7)

How to Multiply Binomials

Binomials are simple algebraic expressions. They are simply two terms joined by a math operator symbol. For the most part, the multiplication of two whole integers or fractions is the same as the multiplication of two binomials.

If the variable that is used in a term is the same as the second term, the exponent attached to each must be different. Another thing about exponents, when it comes to binomials, is that they must be positive (no fractions or negative values). When we are asked to multiply binomials, each term in the first binomial must be multiplied by the second term. This is the most common mistake that I see students make with this skill. They will often leave a term behind. I find it very helpful to have students chart each move they make by drawing lines or arrows. The most common way to achieve this is to use the FOIL (First-Outer-Inner-Last) method. This says to multiply: 1) the first term of each binomial. 2) the outer terms of each component. 3) the inner term of each. 4) the last term of each component. You end off by just combining everything.

The following are the common methods that are use to multiply binomials:

1. The FOIL Method

One of the easiest techniques to multiple two binomials is by using the FOIL method. This is probably why it is also the most often used way of solving these problems. Let's dive into it.

A binomial multiplied by itself produces four terms. FOIL is the abbreviation of the First, Outer, Inner, and Last terms of the equation. It's simple to recall the acronym FOIL, as it helps you locate all four products. If you want to multiply binomials, you need to start by multiplying the first terms, then outer terms, then move on to inner terms, and end with the last terms. This is an excellent method to yield results.

For instance:


In this case, the a from the first parenthesis will be multiplied by the "a" from the second parenthesis, which results in a2. This means you have to multiply the first terms. Then the "a" from the first parenthesis will be multiplied by the "b" from the parenthesis, keeping the minus sign intact. It means you have to multiply outer terms.

Then you have to multiply inner terms. In this case, 2 from the first parenthesis will be multiplied by a from the second parenthesis, resulting in 2a. In the end, you will have to multiply the last terms. In this case, 2 from the first parenthesis will be multiplied by the b from the second parenthesis, keeping the minus sign intact.

The result will be:

a2 – ab + 2a – 2b

2. Distributive Property

The distributive property of multiplication can be used twice to multiply binomials. The following procedures will be used to multiply two binomials (a + 2) and (a + 3).

We'll take the first term in each binomial and multiply them together, which is a (a + 3). Two binomials will be multiplied together in this step: a (a + 3) and 2(a + 3), respectively. The equation will become a (a + 3) + 2(a + 3). It is the sum of the values from parenthesis.

As the last step, you will have to use the distributive principle to extend each of the expressions in the form a(a + 3), which gives you the following: (a2 + 3a) and (2a +6).

The result will be:

A2 + 3a + 2a +6 = a2 + 5a + 6

3. Generic Formulas

In some circumstances you can use generic formulas to your advantage. Rather than computing FOIL every time, a general formula allows you to input your numbers. It's easy to fit binomials raised to the second or third power into an existing formula, resulting in a rapid and simple solution.

You can use variables to replace all of the integers in the formula. Plugging in your numbers to get a response will then be possible at the end. It's possible that there is no number in the equation, in which case the constant being added or subtracted is equal to 1.

4. Squaring Binomials

Remember that squaring a number is simply multiplying it by itself, even though it appears more complicated. The product of two independent variables is equal to the product you get while multiplying them by each other. The new equation can be solved using FOIL.

Advanced Information: Multiplication and division are hyper-2 operations, whereas exponents and radicals are hyper-3 operations. If there are exponents, multiplication and division properties don't apply.