Adding & Subtracting Algebraic Expressions Revision Notes for Leaving Cert Mathematics

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.

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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)

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)

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)

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

Adding & Subtracting Algebraic Expressions (Leaving Cert Mathematics): Revision Notes

Adding & Subtracting Algebraic Expressions

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