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:$(x+1)(x+2)=x\mathrm{²}+2x+x+2=x\mathrm{²}+3x+2$

Key reminders:

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