Correct Answer

📐 MA • Math Direct FormulaMathematicsAlgebra

Option A

809975

Quick Summary:

Given: Two numbers to be multiplied are 895 and 905.

📐MAMath SolutionDirect Formula

📋 Given

Two numbers to be multiplied are 895 and 905.

🔢 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

Express the numbers as $(900 - 5) \times (900 + 5)$ . The result is simply $900^2 - 5^2$ , which is $810000 - 25 = 809975$ .

⚠️ Common Student Trap / Pitfall

Students often perform long multiplication (895 * 905) which consumes time and increases the risk of calculation errors in the middle steps.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify the pattern

Observe that both numbers are equidistant from 900. Thus, we write them as $895 = 900 - 5$ and $905 = 900 + 5$ .

(900−5)(900+5)(900 - 5)(900 + 5)(900−5)(900+5)

Apply the identity

Use the difference of squares identity $(a - b)(a + b) = a^2 - b^2$ , where $a = 900$ and $b = 5$ .

9002−52900^2 - 5^29002−52

Calculate the squares

Square 900 to get 810000 and square 5 to get 25.

810000−25810000 - 25810000−25

Final subtraction

Subtract 25 from 810000 to arrive at the final product.

810000−25=809975810000 - 25 = 809975810000−25=809975

✅

B is correct because the expression $900^2 - 5^2$ results in $810000 - 25 = 809975$ . Note: The provided official answer key label 'A' is incorrect based on mathematical calculation; the correct value matches option B.

Core Concepts Used

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Algebraic Identities Difference of Squares Mental Arithmetic

💡 EXAM TIP

This identity is extremely useful in Data Interpretation sections for quick estimation of product growth or calculating differences in percentage increase problems.

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