Year 7: Simplification and Expansion of Algebraic Expressions

Collecting Like Terms (Simplifying)

Like terms are terms that have the same variable and power. You can combine them by adding or subtracting.

Examples:

• 2x + 3x = 5x (both have x, so combine the numbers)
• 5y + 2y - y = 6y (all have y)
• 3a + 2b + a = 4a + 2b (a terms combine, b stays separate)

Removing Brackets (Expanding)

When you multiply a bracket by a number or variable, distribute that number/variable to every term inside the bracket.

Rule: a(b + c) = ab + ac

Examples:

• 2(x + 3) = 2x + 6 (multiply 2 by each term)
• 3(2y - 1) = 6y - 3 (multiply 3 by each term)
• -2(a + 4) = -2a - 8 (negative multiplies to all terms)

Steps for Simplification

1. Identify like terms (same variable and power)
2. Add or subtract the coefficients
3. Keep the variable and power the same