4.1Basic Algebraic Concepts and Notations

• Specific unknown numbers: e.g. $x - 3 = 7$, so $x = 10$
• Generalised numbers: e.g. $a + b = b + a$ (commutative law, true for all $a$ and $b$)
• Variables: e.g. $P = 4l$ (perimeter of a square changes as length $l$ changes)

Algebraic notations

• $3x$ means $3 \times x$ (omit the multiplication sign)
• $xy$ means $x \times y$
• $\frac{x}{y}$ means $x \div y$
• $x^3$ means $x \times x \times x$

Algebraic expressions and terms

• The coefficient of $x$ in $2x$ is $2$.
• A constant term has no variable (e.g. $7$).
• A linear expression in $x$ contains at most the first power of $x$ (no $x^2$, $x^3$, etc.).