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

Related Topics: More Algebra Lessons

### Multiplying Algebraic Expressions

**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.

Examples:

1. 3a^{2}(-5a^{4})

2. -2c^{2}(-7c^{3}x^{5})(bx^{2})^{2}

3. 3a^{3}(-ab^{4})(2a^{2}c^{3})

**How to multiply algebraic expressions?**

Using the distributive law to multiply algebraic expressions:

1. 3sy(s - t)

2. 4uv^{2}(3^{2}z - 7u^{3})

**How to multiply expressions using the distributive law?**

Solve the following questions

1. 3cy^{2}(-4cx - 2xy^{3})

2. (x + 5)(x - 2)

**Multiplication of Algebraic Expressions - Solving Complex Questions**

Examples:

1. (b + 3c)^{2}

2. (2y - 4)^{3}

### Dividing Algebraic Expressions

**How to divide algebraic terms or variables?**
**How to divide Algebraic Expressions?**

**How to divide algebraic terms or variables?**

Examples:

1. -8x^{5} ÷ - 5x^{3}

2. -4x^{3} ÷ 7x^{9}
**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.

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.

Related Topics: More Algebra Lessons

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

*Example : *

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

* Solution:*

–2*a*^{3}*b**× *3*ab*^{2}*c
*= –2

1. Multiply the numbers (coefficients)

2. Multiply the variables - exponents can be combines if the base is the same.

Examples:

1. 3a

2. -2c

3. 3a

Using the distributive law to multiply algebraic expressions:

1. 3sy(s - t)

2. 4uv

Solve the following questions

1. 3cy

2. (x + 5)(x - 2)

Examples:

1. (b + 3c)

2. (2y - 4)

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

**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.

**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

* Solution: *

Examples:

1. -8x

2. -4x

Examples of dividing variables and dividing polynomials

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.

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