Multiplying Algebraic 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.

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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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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