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Multiplying and Dividing Algebraic Expressions




 

In these lessons, we will learn how to multiply and divide algebraic expressions.

Related Topics: More Algebra Lessons

Multiplying Algebraic Expressions

We can multiply two algebraic terms to get a product, which is also an algebraic term.

Example :

Evaluate 3pq3× 4qr

Solution:

3pq3× 4qr
= 3 × p × q × q × q × 4 × q × r
= 3 × 4 × p × q × q × q × q × r
= 12 × p × q4 × r
= 12pq4r


Example :

Evaluate –2a3b× 3ab2c

Solution:

–2a3b× 3ab2c
= –2 × 3× a3× a × b × b2× c
= –6× a4× b3× c
= –6a4b3c

The following video shows how to multiply algebraic terms or variables.
How to multiply expressions using the distributive law?



Algebra - Multiplication of Algebraic Expressions - Solving Questions.
Algebra - Multiplication of Algebraic Expressions - Solving Complex Questions.


 

Dividing Algebraic Expressions

We can divide an algebraic term by another algebraic term to get the quotient. The steps below show how the division is carried out.

How to divide algebraic terms or variables?

Step 1: Write the division of the algebraic terms as a fraction.
Step 2:Simplify the coefficient.
Step 3: Cancel variables of the same type in the numerator and denominator.


How to divide Algebraic Expressions?

Step 1:Factorize the algebraic expressions.
Step 2: Cancel factors in the numerator and denominator where possible.

Example :

Evaluate 6pq3 ÷ 3pq

Solution:

Example :

Evaluate –8a3bc ÷ 2ab

Solution:



The following video shows how to divide algebraic terms or variables.
Multiplying & Dividing Algebraic Fractions


 
Algebra - Division of Algebraic Expressions - Solving Questions.
Algebra - Division of Algebraic Expressions - Practice Questions.



You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.


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