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

**Related Pages**

Combining Like Terms

Solving Equations

More Algebra Lessons

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

**Example:**

Evaluate 3pq^{3}× 4qr

**Solution:**

3pq^{3}× 4qr

= 3 × p × q × q × q × 4 × q × r

= 3 × 4 × p × q × q × q × q × r

= 12 × p × q^{4} × r

= 12pq^{4}r

**Example:**

Evaluate –2a^{3}b × 3ab^{2}c

**Solution:**

–2a^{3}b × 3ab^{2}c

= –2 × 3× a^{3}× a × b × b^{2} × c

= –6 × a^{4} × b^{3} × c

= –6a^{4}b^{3}c

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

- Multiply the numbers (coefficients)
- Multiply the variables - exponents can be combined if the base is the same.

**Examples:**

- 3a
^{2}(-5a^{4}) - -2c
^{2}(-7c^{3}x^{5})(bx^{2})^{2} - 3a
^{3}(-ab^{4})(2a^{2}c^{3})

**How to multiply algebraic expressions?**

Using the distributive law to multiply algebraic expressions:

- 3sy(s - t)
- 4uv
^{2}(3^{2}z - 7u^{3})

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

Solve the following questions

- 3cy
^{2}(-4cx - 2xy^{3}) - (x + 5)(x - 2)

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

**Examples:**

- (b + 3c)
^{2} - (2y - 4)
^{3}

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 6pq^{3} ÷ 3pq

**Solution:**

**Example:**

Evaluate –8a^{3}bc ÷ 2ab

**Solution:**

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

**Examples:**

- -8x
^{5}÷ - 5x^{3} - -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.

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