Misconception Buster: Myth vs Truth

ROLE: Act as a concept-clarity teacher who busts maths misconceptions with proof.

CONTEXT: This is for [CLASS/GRADE] students in [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE]. Topic: [TOPIC]. My students keep believing this wrong thing: [THE WRONG BELIEF e.g. (a+b)^2 = a^2 + b^2]. I want to kill the misconception cleanly.

YOUR TASK:
1. State the misconception plainly, then the correct truth.
2. Prove the truth with a concrete numerical counterexample that exposes the myth.
3. Explain WHY the wrong belief is so tempting.
4. Add a few related myths in the same topic so I can pre-empt them too.

INPUT: Here is the topic and the belief to bust: [TOPIC], [THE WRONG BELIEF]. Level: [CLASS/GRADE], [BOARD or EXAM].

HOW TO WORK IT OUT: For each counterexample, compute internally and VERIFY it two independent ways and state them. Use small, clean numbers a student can check mentally. Never invent formulas or rules; name standard results correctly. Keep all maths legible.

OUTPUT FORMAT (exact headings):
1. Myth vs Truth table - columns: Myth | Truth | Quick proof or counterexample.
2. Why the myth tempts us - one short paragraph per myth.
3. The correct rule, stated cleanly - in words and symbols.
4. Three traps disguised as this myth - short examples that look fine but are wrong, with fixes.
5. Classroom mantra - one memorable line students can repeat.
6. Verification note - confirm each counterexample checks out.

RULES: Plain ASCII only, straight quotes. Counterexamples must use real numbers, not vague claims. Keep the tone confident and clear.

FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return one complete, editable document ready to paste into Word or Google Docs. Use a descriptive title, short section headings, readable paragraphs, numbered actions and tables only where they make the material easier to use. Include every requested section; do not return formatting advice instead of the document.


MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.

CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.

GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.

SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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