The correct answer is Option B: 33856. Use $(a-b)^2 = a^2 - 2ab + b^2$ for $184^2$ as $(200 - 16)^2$. This gives $40000 - 6400 + 256 = 33856$. Step-by-Step Solution & Concepts: Shortcut Trick: Use $(a-b)^2 = a^2 - 2ab + b^2$ for $184^2$ as $(200 - 16)^2$. This gives $40000 - 6400 + 256 = 33856$. Formula Used: $$(a+b)^2 = a^2 + 2ab + b^2$$ Given: Number to be squared: 184. Steps: Represent as binomial: To simplify, express 184 as $(200 - 16)$.. Apply expansion formula: Use the algebraic identity $(a - b)^2 = a^2 - 2ab + b^2$ where $a = 200$ and $b = 16$.. Execute calculation: Calculate each part: $200^2 = 40000$, $2 \times 200 \times 16 = 6400$, and $16^2 = 256$.. Final subtraction and addition: Subtract 6400 from 40000 to get 33600, then add 256. Answer: B is correct because the square of 184 is 33856. Exam Tip: This identity-based squaring trick is essential for time management in Quant sections and is often used in compound interest calculations.

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MathematicsPrevious Year Paper 2024

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Evaluate 184 2

33866

33856

33836

33806

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option B

33856

Quick Summary:

Use $(a-b)^2 = a^2 - 2ab + b^2$ for $184^2$ as $(200 - 16)^2$ . This gives $40000 - 6400 + 256 = 33856$ .

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📐MAMath SolutionDirect Formula

📋 Given

Number to be squared: 184.

🔢 Formula Used

(a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2

⚡ Exam Hall Shortcut / Speed Trick

Use $(a-b)^2 = a^2 - 2ab + b^2$ for $184^2$ as $(200 - 16)^2$ . This gives $40000 - 6400 + 256 = 33856$ .

⚠️ Common Student Trap / Pitfall

Students often make calculation errors in manual multiplication like $184 \times 184$ or incorrectly applying $(a+b)^2$ with wrong regrouping.

🔢 Step-by-Step Solution

Represent as binomial

To simplify, express 184 as $(200 - 16)$ .

1842=(200−16)2184^2 = (200 - 16)^21842=(200−16)2

Apply expansion formula

Use the algebraic identity $(a - b)^2 = a^2 - 2ab + b^2$ where $a = 200$ and $b = 16$ .

(200−16)2=2002−2×200×16+162(200 - 16)^2 = 200^2 - 2 \times 200 \times 16 + 16^2(200−16)2=2002−2×200×16+162

Execute calculation

Calculate each part: $200^2 = 40000$ , $2 \times 200 \times 16 = 6400$ , and $16^2 = 256$ .

40000−6400+25640000 - 6400 + 25640000−6400+256

Final subtraction and addition

Subtract 6400 from 40000 to get 33600, then add 256.

33600+256=3385633600 + 256 = 3385633600+256=33856

✅

B is correct because the square of 184 is 33856.

Core Concepts Used

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Algebraic Identities Squaring Numbers Binomial Expansion

💡 EXAM TIP

This identity-based squaring trick is essential for time management in Quant sections and is often used in compound interest calculations.

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