Last Updated Sep 27, 2025

Adding & Subtracting Algebraic Expressions Simplified Revision Notes for Leaving Cert Mathematics

Revision notes with simplified explanations to understand Adding & Subtracting Algebraic Expressions quickly and effectively.

Learn about The Basics for your Leaving Cert Mathematics Exam. This Revision Note includes a summary of The Basics for easy recall in your Mathematics exam

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Adding & Subtracting Algebraic Expressions

Adding and subtracting algebraic expressions involves combining like terms while preserving the mathematical structure. It's a fundamental skill in algebra and is essential for solving equations, simplifying expressions, and manipulating formulas.

infoNote

Like terms are terms that have the same variables raised to the same powers.

For instance :

• $3x^2$ and $-2x^2$ are like terms.
• $a$ and $b$ are not like terms.
• $3$ and $6$ are like terms.

Example

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Simplify the following expression :

$$(3x^2 + 2x + 1) + (5x^2 - x + 4)$$

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Remove Parentheses :

$$3x^2 + 2x + 1 + 5x^2 - x + 4$$

Group Like Terms :

$$(3x^2 + 5x^2) + (2x - x) + (1 + 4)$$

Combine Like Terms :

$$8x^2 + x + 5$$

Example

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Simplify the following expression :

$$(4x^2 - 3x + 7) - (2x^2 + x - 5)$$

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Remove Parentheses and Change Signs :

$$4x^2 - 3x + 7 - 2x^2 - x + 5$$

Group Like Terms :

$$(4x^2 - 2x^2) + (-3x - x) + (7 + 5)$$

Combine Like Terms :

$$2x^2 - 4x + 12$$

Example

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Simplify the following expression :

$$(2x + 3y - 5) + (4x - y + 2)$$

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Remove Parentheses and Change Signs :

$$2x + 3y - 5 + 4x - y + 2$$

Group Like Terms :

$$(2x + 4x) + (3y - y) + (-5 + 2)$$

Combine Like Terms :

$$6x + 2y - 3$$

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