Find the value of $ (10001 + 12)(10001 - 12) $. | Mathematics MCQ | Examoogle

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Find the value of $(10001 + 12)(10001 - 12)$ .

1000019857

10019857

1000190857

100019857

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option D

100019857

Quick Summary:

Use the algebraic identity $(a+b)(a-b) = a^2 - b^2$ where $a = 10001$ and $b = 12$ . Calculate $10001^2 = 100020001$ and $12^2 = 144$ , then subtract.

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📐MAMath SolutionDirect Formula

📋 Given

The expression to evaluate is (10001 + 12)(10001 - 12).

🔢 Formula Used

(a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2(a+b)(a−b)=a2−b2

⚡ Exam Hall Shortcut / Speed Trick

Use the algebraic identity $(a+b)(a-b) = a^2 - b^2$ where $a = 10001$ and $b = 12$ . Calculate $10001^2 = 100020001$ and $12^2 = 144$ , then subtract.

⚠️ Common Student Trap / Pitfall

Students often try to expand it by full multiplication instead of recognizing the difference of squares identity, leading to calculation errors.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify the pattern

The given expression $(10001 + 12)(10001 - 12)$ matches the algebraic identity $(a + b)(a - b) = a^2 - b^2$ .

(a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2(a+b)(a−b)=a2−b2

Substitute values

Substitute $a = 10001$ and $b = 12$ into the formula.

(10001+12)(10001−12)=100012−122(10001 + 12)(10001 - 12) = 10001^2 - 12^2(10001+12)(10001−12)=100012−122

Perform the calculation

Calculate $10001^2 = (10000 + 1)^2 = 100000000 + 20000 + 1 = 100020001$ . Then subtract $12^2 = 144$ .

100020001−144=100019857100020001 - 144 = 100019857100020001−144=100019857

✅

D is correct because the result of the calculation $(10001^2 - 12^2)$ is 100019857.

Core Concepts Used

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Algebraic Identities Difference of Squares Arithmetic Calculation

💡 EXAM TIP

This identity is frequently used in mental math and simplification problems in RRB and SSC exams to quickly evaluate large numbers by shifting them close to powers of 10.

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