Simplifying expressions

Description

Simplifying an algebraic expression means collecting like terms and writing it in its most compact form.

Like terms share the same variable(s) and power(s). Only like terms can be added or subtracted.

Examples: $$3x + 5x = 8x$$ $$7x^2 - 2x^2 = 5x^2$$ $$4x + 3y - x + 2y = 3x + 5y$$

Mixed expressions: $$2x^2 + 3x - x^2 + 5 - x = x^2 + 2x + 5$$

Key rules:

• $x$ means $1x$ — the coefficient of 1 is invisible
• $x^2$ and $x$ are NOT like terms — different powers
• Terms with different variables ($x$ and $y$) are NOT like terms

Simplifying with multiplication: expand first, then collect. $$2(3x + 1) + 3(x - 4) = 6x + 2 + 3x - 12 = 9x - 10$$

Common error: adding unlike terms — $3x + 2y \ne 5xy$.

Links

Expanding single brackets Expanding quadratics Substitution