Multiplying and Dividing Algebraic Expressions

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

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Related Pages
Combining Like Terms
Solving Equations
More Algebra Lessons

Multiplying Algebraic Expressions

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

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

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 combined 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.

Evaluate 6pq3 ÷ 3pq

divide algebraic expressions

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.

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