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Multiplying Terms in Algebra

(KS3, Year 7)

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.

Question

Multiply the two terms below. multiply terms example

Step-by-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

2

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

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

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. multiply_terms_example_step_4

5

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

Answer:

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.

Question

Multiply the two terms below. multiply terms example 2

Step-by-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

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

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

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. multiply_terms_example_2_step_4

5

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

Answer:

We have multiplied the terms together:
2ab × −ac2 = −2a2bc2

Lesson Slides

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

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
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This page was written by Stephen Clarke.

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