Multiplying Algebraic Expressions

Multiplying algebraic expressions involves using the distributive property and the rules of exponents. Then, combine like terms to simplify the result.

The following diagram shows how to multiply algebraic expressions. Scroll down the page for more examples and solutions on how to multiply expressions.

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.

Algebra Math Worksheets
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Printable & Online Algebra Worksheets

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)
= 2y² + 5y – 6y – 15
= 2y² – y – 15

b) (a + b)²
= (a + b)(a + b) = a(a + b) + b(a + b)
= a² + ab + ab + b²
= a² + 2ab + b²

Multiplication of Algebraic Expressions:

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

Example:

1. -2c²(-7c³x⁵)(bx²)² =
2. 3a²(-ab⁴)(2a²c³) =
3. 3sy(s - t) =
4. 4uv²(3u²z - 7u³) =

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Examples of multiplying expressions using the distributive property
Example:

1. (x + 2)(x + 3)
2. (5x + 9)(4x - 2)
3. (2x + y)(3x + 2y)
4. (2x + 2)²

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Multiplication of Algebraic Expressions - Use the distributive property
Example:

1. 3cy²(-4cx - 2xy³)
2. (x + 5)(x -2)

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Multiplication of Algebraic Expressions - Solving Complex Questions
Example:

1. (b + 3c)²
2. (2y - 4)³

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