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Multiplying Terms in Algebra
(KS3, Year 7)
The Lesson
Terms can be multiplied. Imagine we wanted to multiply the terms 2a and 3b.How to Multiply Terms in Algebra
Multiplying terms is easy.Question
Multiply the two terms below.StepbyStep:
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: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:

b only appears in 3b. b will appear in the answer:
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.
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.StepbyStep:
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 × −ac^{2} = 2ab × −1ac^{2}
2 × 1 = 2
2 will appear in the answer:2
Multiply the letters that appear in both terms. In our example, a appears in both terms.
2ab × −ac^{2}
a × a = a^{2}
Don't forget: = a × a = a^{2} (a squared).
a^{2} will appear in the answer:3
Find letters that only appear in one term.

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

c only appears in −ac^{2}. It appears with an exponent of 2: c^{2} (c squared). c^{2} will appear in the answer:
4
Write the results from the previous steps next to each other.
2 was the result of Step 1. a^{2} was the result of Step 2. b and c^{2} were the result of Step 3.
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 × −ac^{2} = −2a^{2}bc^{2}
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.Top Tip
Rules For Signs: Multiplication
Same signs give a plus:Different signs give a minus:
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