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

**Related Pages**

Algebraic Expressions

Adding And Subtracting Algebraic Expressions

More Algebra Lessons

The following diagram shows some expansions, that are useful to remember, when multiplying two algebraic expressions or binomials. Scroll down the page for more examples and solutions on how to expand expressions.

**How to Multiply a Term and an Algebraic Expression?**

We will first consider examples of multiplying a term and an algebraic expression.

**How to Multiply Two Algebraic Expressions?**

Next, we will also consider the multiplication of two algebraic expressions: (a + b)(c + d)

Such an operation is called ‘**expanding the expression**’.

To expand the expression, we multiply each term in the first pair of brackets by every term in
the second pair of brackets.

**Example:**

Expand the following:

a) (y – 3)(2y + 5)

b) (a + b)^{2}

**Solution:**

a) (y – 3)(2y + 5)

= y(2y+ 5) – 3(2y + 5)

= (y × 2y) + (y × 5) + (–3 × 2y) + (–3 × 5)

= 2y^{2} + 5y – 6y – 15

= 2y^{2} – y – 15

b) (a + b)^{2}

= (a + b)(a + b) = a(a + b) + b(a + b)

= a^{2} + ab + ab + b^{2}

= a^{2} + 2ab + b^{2}

**Multiplication of Algebraic Expressions:**

- Multiply the numbers (numerical coefficients)
- Multiply the letters (literal numbers) - Exponents can only be combined if the base is the same.

**Example:**

- -2c
^{2}(-7c^{3}x^{5})(bx^{2})^{2}= - 3a
^{2}(-ab^{4})(2a^{2}c^{3}) = - 3sy(s - t) =
- 4uv
^{2}(3u^{2}z - 7u^{3}) =

**Examples of multiplying expressions using the distributive property**

**Example:**

- (x + 2)(x + 3)
- (5x + 9)(4x - 2)
- (2x + y)(3x + 2y)
- (2x + 2)
^{2}

**Multiplication of Algebraic Expressions - Use the distributive property**

**Example:**

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

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

**Example:**

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

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