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How to Multiply Terms in Algebra (Mathematics Lesson)

Multiplying Terms in Algebra

Terms can be multiplied.

Imagine we wanted to multiply the terms 2a and 3b.

2 a times 3 b

How to Multiply Terms in Algebra

Multiplying terms is easy.

An Example Question

Multiply the two terms below.

Step 1

Multiply the numbers that appear in the terms. In our example, the numbers are 2 and 3.

2a × 3b

2 × 3 = 6

6 will appear in the answer:

6
Step 2

Multiply the letters that appear in both terms. In our example, no letter appears in both terms.

Step 3

Find letters that only appear in one term.

a only appears in 2a. a will appear in the answer:

a

b only appears in 3b. b will appear in the answer:

b
Step 4

Write the results from the previous steps next to each other.

6 was the result of Step 1. a and b were the result of Step 3.

Step 5

Check the signs. In our example, both terms are positive, so their product is positive.

We have multiplied the terms together:

2a × 3b = 6ab

A Real Example of How to Multiply Terms in Algebra

This is a more complicated example.

An Example Question

Multiply the two terms below.

Step 1

Multiply the numbers that appear in the terms. In our example, the number is 2 in one term. The other does not appear to have a number, which means it actually has a number of 1.

2ab × -ac2 = 2ab × -1ac2

2 × 1 = 2

2 will appear in the answer:

2
Step 2

Multiply the letters that appear in both terms. In our example, a appears in both terms.

2ab × -ac2

a × a = a2

Don't forget: = a × a = a2 (a squared).

a2 will appear in the answer:

a squared
Step 3

Find letters that only appear in one term.

b only appears in 2ab. b will appear in the answer:

b

c only appears in -ac2. It appears with an exponent of 2: c2 (c squared). c2 will appear in the answer:

c squared
Step 4

Write the results from the previous steps next to each other.

2 was the result of Step 1. a2 was the result of Step 2. b and c2 were the result of Step 3.

Step 5

Check the signs. In our example, one terms is positive, the other negative. Their product is negative.

We have multiplied the terms together:

2ab × -ac2 = -2a2bc2

Another Real Example of How to Multiply Terms in Algebra

The slider below shows a real example of how to multiply terms in algebra.

Curriculum
Algebra Lessons
Interactive Test
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Here's a second test on multiplying terms.
Here's a third test on multiplying terms.

Note

What Is a Term in Algebra?

A term is a collection of numbers, letters and brackets all multiplied together.

Multiplying the Same Letter Using Exponent Notation

There is a law for multiplying terms with exponents. Add the exponents to each other.

to multiply terms with exponents, add the exponents
Top Tip

Rules For Signs: Multiplication

Same signs give a plus:

multiply the same signs gives a positive product

Different signs give a minus:

multiply different signs gives a negative product