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Year 7: Simplification and Expansion of Algebraic Expressions (Level 2)

Quick Reference

Like Terms: Must have same variable AND same power
Simplify: Combine coefficients of like terms
Expand: Multiply term outside bracket by every term inside

Simplifying with Multiple Variables and Powers

When simplifying more complex expressions, group like terms carefully.

Examples:

$2 x^{2} + 3 x + 5 x - x^{2} = x^{2} + 8 x$ (combine x² terms, then x terms)
$4 a + 2 b - 3 a + b = a + 3 b$ (a's together, b's together)
$3 x y - y + 2 x y + 4 y = 5 x y + 3 y$ (xy's together, y's together)

Expanding More Complex Expressions

Remember to multiply the term outside by EVERY term inside the bracket.

Examples:

$2 (x + 3 y) = 2 x + 6 y$
$3 (2 a - b) = 6 a - 3 b$
$- 1 (x - 5) = - x + 5$
$4 (2 x + 3 y - 1) = 8 x + 12 y - 4$

Multi-Step Simplification

Sometimes you need to expand first, then simplify:

Example: $2 (x + 3) + 3 x$

Expand: $2 x + 6 + 3 x$
Combine like terms: $5 x + 6$

Common Mistakes:

Combining different powers: x and x² cannot be combined
Missing terms when expanding: $3 (2 x + 5 - y)$ must expand all three terms
Sign errors with negatives: $- 3 (x - 2) = - 3 x + 6$ (not -3x - 6)