OML Search

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


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


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

How to multiply algebraic terms or variables?
1. Multiply the numbers (coefficients)
2. Multiply the variables - exponents can be combines if the base is the same.
1. 3a2(-5a4)
2. -2c2(-7c3x5)(bx2)2
3. 3a3(-ab4)(2a2c3)

How to multiply algebraic expressions?
Using the distributive law to multiply algebraic expressions:
1. 3sy(s - t)
2. 4uv2(32z - 7u3)
How to multiply expressions using the distributive law?
Solve the following questions
1. 3cy2(-4cx - 2xy3)
2. (x + 5)(x - 2)

Multiplication of Algebraic Expressions - Solving Complex Questions
1. (b + 3c)2
2. (2y - 4)3


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


Example :

Evaluate –8a3bc ÷ 2ab


How to divide algebraic terms or variables?
1. -8x5 ÷ - 5x3
2. -4x3 ÷ 7x9 Multiplying & Dividing Algebraic Fractions
Examples of dividing variables and dividing polynomials

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

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

OML Search

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

[?] Subscribe To This Site

follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines