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.Step-by-Step:
1
Multiply the numbers that appear in the terms. In our example, the numbers are 2 and 3.
6 will appear in the answer:
2a × 3b
2 × 3 = 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:
- 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.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.
2 will appear in the answer:
2ab × −ac^{2} = 2ab × −1ac^{2}
2 × 1 = 2
2
Multiply the letters that appear in both terms. In our example, a appears in both terms.
Don't forget: = a × a = a^{2} (a squared).
a^{2} will appear in the answer:
2ab × −ac^{2}
a × a = a^{2}
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}