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 combined 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.

Related Topics: 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

1. Multiply the numbers (coefficients)

2. Multiply the variables - exponents can be combined 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 6pq^{3} ÷ 3pq

Solution:

Example:

Evaluate –8a^{3}bc ÷ 2ab

Solution:

Examples:

1. -8x

2. -4x

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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