# 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 3*pq*^{3}*×* 4*qr *

* Solution:*

3*pq*^{3}*×* 4*qr*

= 3 *× p × q × q × q × *4 *× q × r *

= 3 *× *4 *× p × q × q × q × q × r*

= 12 *× p × q*^{4} *× r *

= 12*pq*^{4}*r*

*Example : *

Evaluate –2*a*^{3}*b**× *3*ab*^{2}*c *

* Solution:*

–2*a*^{3}*b**× *3*ab*^{2}*c*

= –2 *× *3*× a*^{3}*× a × b × b*^{2}*× c *

*=* –6*× a*^{4}*× b*^{3}*× c *

= –6*a*^{4}*b*^{3}*c *

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 6*pq*^{3} ÷ 3*pq*

* Solution: *

* ***Example*** : *

Evaluate –8*a*^{3}bc ÷ 2*ab*

* 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.

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