Year 10: Simplification and expansion of algebraic expressions

This cheat-sheet covers the basics of simplifying and expanding algebraic expressions. It’s designed for Year 10 students in Australia.

Simplifying expressions

• Combining like terms: Add or subtract terms with the same variables and powers. Example: 2x + 3x = 5x
• Distribution: Multiply a number or variable by each term inside parentheses. Example: 2(x + 3) = 2x + 6
• Removing brackets: Use the distributive property to get rid of brackets.

Expanding expressions

• Linear expressions: Expressions with one unknown variable (e.g., 3x + 2). Simplifying is usually the key.
• Binomials: Expressions with two terms (e.g., x² + 2x + 1). Expanding involves distributing.
• Example: (x + 1)(x + 2) = x² + 2x + x + 2 = x² + 3x + 2

Key reminders:

• Always simplify before expanding.
• Be careful with negative signs.
• Check your work by substituting a value for the variable.