Algebraic expressions practice

Algebraic notation

• Drop the × sign and write numbers first: $a \times 3 \times b = 3ab$
• Write repeated factors as powers: $x \times x \times 4 = 4x^2$
• Do not write a coefficient of $1$: $y \times (-1) \times x = -xy$
• Write division as a fraction: $x \div 5 = \frac{x}{5}$

The signs $+$ and $-$ cannot be dropped: $a \times 2 - b \div 3 = 2a - \frac{b}{3}$.

Substitution

Replace each letter by its value, putting negative numbers in brackets.

Example: if $a = -2$, then $a^2 - 3a = (-2)^2 - 3 \times (-2) = 4 + 6 = 10$.

Simplifying linear expressions

Collect like terms: $3x + 5 - 7x + 2 = -4x + 7$. Expand brackets with the distributive law, changing every sign inside a bracket preceded by a minus sign.

For fractions, use a common denominator and keep each numerator in brackets: $\frac{x + 1}{2} - \frac{x - 2}{3} = \frac{x + 7}{6}$.

Writing expressions

First write a word equation such as cost = price × quantity, then substitute.

• 4 apples at $a$ yen and 9 oranges at $b$ yen cost $(4a + 9b)$ yen.
• $x$ yen with $20\%$ off is $\frac{4}{5}x$ yen.
• The two-digit number with tens digit $a$ and ones digit $b$ is $10a + b$.