Year 9: Simplification and expansion of algebraic expressions

Simplification

Simplifying an expression means making it shorter and easier to understand. You do this by removing brackets and combining like terms.

Combining Like Terms

Like terms have the same variable(s) raised to the same power (e.g., 3x and 5x are like terms). You can only add or subtract like terms.

Example: 2x + 3x - x = (2+3-1)x = 4x

Example: 3x² + 2x² - x² = (3+2-1)x² = 4x²

Expansion (Brackets)

Expansion means multiplying a single term by an entire expression inside brackets.

The Distributive Property

This is key! a(b + c) = ab + ac. You multiply 'a' by each term inside the brackets.

Example: 2(x + 3) = 2 * x + 2 * 3 = 2x + 6

Example: 3(2x - 1) = 3 * 2x - 3 * 1 = 6x - 3

Important Notes

• Remember to multiply the number outside the brackets by each term inside.
• Always check your answer by expanding it back to see if you get the original expression.