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