Algebra

• Only like terms combine. 5a and −2a combine; 3a and 4b do not.
• A minus sign in front of a bracket flips every sign inside it: 3(x+2) − 2(x−1) = 3x + 6 − 2x + 2 = x + 8.
• Multiplying terms: multiply the numbers, then the letters. 4a × 3a = 12a².
• The coefficient includes the sign. In 5x² − 3x + 7 the coefficient of x is −3.
• The degree is the highest power, not the number of terms.

• Whatever you do to one side, do to the other.
• Moving a term across the equals sign changes its sign.
• Gather the unknowns on one side and the numbers on the other, then divide by the coefficient — and do not stop before that last division.
• Always check by substituting the answer back in.

• (a + b)² = a² + 2ab + b²
• (a − b)² = a² − 2ab + b²
• a² − b² = (a + b)(a − b)
• The middle term 2ab is the one people drop. (a+b)² is not a² + b².

• 'A number' → n. 'Twice a number' → 2n. 'Seven less than twice a number' → 2n − 7.
• 'Seven less than x' is x − 7, not 7 − x. The order matters and the words reverse it.
• Consecutive numbers: n, n+1, n+2. Their sum is 3n + 3.
• Read the question again at the end. If it asks for x², answering x is a wasted mark.

These are the mistakes, not the rules — each one is something a student who knows the topic still does under time pressure.

1. Writing (a+b)² = a² + b². The 2ab term is the whole point of the identity.
2. Multiplying the indices when the bases are multiplied. 2³ × 2² is 2⁵, not 2⁶.
3. Cubing only the letter in (2x)³. The power applies to the 2 as well: 8x³.
4. Stopping one step early — leaving the answer as 3x = 15 instead of x = 5.
5. Reading 'seven less than twice a number' as 7 − 2n.