Basic arithmetic operations (addition, subtraction, multiplication, division) can be applied to algebraic expressions, but only to like terms. Unlike terms cannot be directly combined.

Combine like terms by adding or subtracting their coefficients. Unlike terms remain separate.

Examples:

• 3x + 5x + 2x = (3+5+2)x = 10x


• 2y² + 7y² - 3y² = (2+7-3)y² = 6y²


• 5ab + 3ab + ab = (5+3+1)ab = 9ab


• 6m - 4m + 2m = (6-4+2)m = 4m


• -3x + 7x - 2x = (-3+7-2)x = 2x


• 10p + (-4p) + 6p = (10-4+6)p = 12p

Addition and Subtraction of Algebraic Expressions

Rule: Add or subtract only coefficients of like terms; variables remain unchanged.

Examples:

• 7x + 3x = 10x


• 10y² - 6y² = 4y²


• 9ab - 4ab = 5ab


• 6m + (-10m) = -4m


• 5x - (-3x) = 8x


• -7p + 2p = -5p

Multiplication of Algebraic Expressions (Like Terms)

Multiply coefficients and add powers of variables.

Examples:

• 3x × 4x = 12x²


• 2y² × 5y² = 10y⁴


• 6a × 3a = 18a²


• -2m × 5m = -10m²


• 4p × (-3p) = -12p²


• 2x² × 3x² = 6x⁴

Division of Algebraic Expressions (Like Terms)

Divide coefficients and subtract powers of variables.

Examples:

• 12x² ÷ 3x = 4x


• 10y⁴ ÷ 5y² = 2y²


• 18a² ÷ 6a = 3a


• -10m² ÷ 5m = -2m


• -12p² ÷ 4p = -3p


• 6x⁴ ÷ 3x² = 2x²

Important Notes

• Only like terms can be combined; unlike terms stay separate.


• Multiplication and division can change powers of variables.


• Always simplify expressions by collecting like terms first before applying other operations.