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Home >> Polynomials >> Algebraic Expression >> Terms of Algebraic Expression >> Like Terms >> Multiplication of Like Terms >>

Multiplication of Like Terms

Addition of Like Terms Subtraction of Like Terms Multiplication of Like Terms

Before you study what is multiplication of like terms, you are advised to read:

What are Like Terms ?
What are Constants ?
What are Variables ?
How to Multiply Constant & Variable ?
How to Multiply Integers ?
Law of Exponent am X an = am+n

Following examples will help you understand this concept:

Example 1: Multiply b and b
Solution: Both the terms are like terms
Power of both term is 1

Now as per the Law of exponent, am X an = am+n, we get:
b1 X b1 = b2

Hence, b X b = b2



Example 2: Multiply 2q and 4q
Solution: As per the given question, both the given terms are like terms

Write terms in the multiplication expression and we get:
2q X 4q

Multiply constants and variable separately, as shown below:
(2 X 4) X (q X q)

Multiply constants as we multiply numbers and we get:
(8) X (q X q)

Multiply variables as per the Law of exponent, am X an = am+n, we get:
8 X q2

Multiply constant and variable and we get:
8q2

Hence, (2q X 4q) = 8q2



Example 3: Multiply 5a2 and 7a2
Solution: As per the given question, both the given terms are like terms

Write terms in the multiplication expression and we get:
5a2 X 7a2

Multiply constants and variable separately, as shown below:
(5 X 7) X (a2 X a2)

Multiply constants as we multiply numbers and we get:
(35) X (a2 X a2)

Multiply variables as per the Law of exponent, am X an = am+n, we get:
35 X a4

Multiply constant and variable and we get:
35 a4

Hence, (5a2 X 7a2) = 35a4



Example 4: Multiply -p3 and 3p3
Solution: As per the given question, both the given terms are like terms

Write terms in the multiplication expression and we get:
-p3 X 3p3

Multiply constants and variable separately, as shown below:
(-1 X 3 ) X (p3 X p3)

Multiply constants as we multiply positive and negative integers & we get:
(-3) X (p3 X p3)

Multiply variables as per the Law of exponent, am X an = am+n, we get:
-3 X p6

Multiply constant and variable and we get:
-3p6

Hence, (-p3 X 3p3) = (-3p6)



Example 5: Multiply -5ab3 and -2ab3
Solution: As per the given question, both the given terms are like terms

Write terms in the multiplication expression and we get:
-5ab3 X -2ab3

Multiply constants and variable separately, as shown below:
(-5 X -2 ) X (a X a) X (b3 X b3)

Multiply constants as we multiply two negative integers and we get:
(-10) X (a X a) X (b3 X b3)

Multiply variables as per the Law of exponent, am X an = am+n, we get:
(-10) X (a2) X (b6)

Multiply constant and variable and we get:
-10a2b6

Hence, (-5ab3 X -2ab3) = (-10a2b6)

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