Year 10: Simplification and expansion of algebraic expressions

Simplification

Expanding Brackets (Distribution)

This is the process of multiplying each term inside the brackets by a common factor. For example: 2(x + 3) = 2x + 6

Combining Like Terms

Like terms have the same variable raised to the same power. Combine them by adding or subtracting their coefficients. Example: 3x + 2x - x = 4x

Examples of Simplification

• 3y + 5y - 2y = 6y
• 4(x + 2) = 4x + 8
• 2x + 3(x - 1) = 2x + 3x - 3 = 5x - 3

Expansion

Expanding Brackets (Distribution) - Reverse of Simplification

Multiplying a single term by an expression inside brackets. For example: 2(x + 3) = 2x + 6

Examples of Expansion

• x(2x + 1) = 2x² + x
• 3(a + b) = 3a + 3b
• -2(x - 3) = -2x + 6

Remember to always multiply each term within the brackets!