Find value 102 x 102 – 98 x 98.

Appeared in: AIIMS Rishikesh & Jodhpur NO - 2017

Explanation

The given expression, 102 × 102 – 98 × 98, is in the form of a2 - b2.
This can be simplified using the algebraic identity for the difference of squares: a2 - b2 = (a - b)(a + b).
In this problem, 'a' is 102 and 'b' is 98.
Substituting these values into the formula gives (102 - 98) × (102 + 98).
Calculating the terms within the parentheses results in 4 × 200.
The final product is 800, which is the correct answer.

Option A: This is an incorrect result, likely due to an arithmetic error during calculation. For instance, incorrectly calculating the sum (102 + 98) as 175 and then multiplying by 4 (4 x 175 = 700).
Option B: This value is incorrect. It may stem from a calculation mistake, such as rounding the sum (102 + 98 = 200) to 250 and then multiplying by the difference (4), resulting in 1000.
Option D: This is an incorrect result. An error such as miscalculating the difference (102 - 98) as 6 instead of 4, and then multiplying by the sum (200), would lead to 1200.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Algebraic Identities (Difference of Squares) as background academic context rather than a clinical decision trigger.
While this is a general mathematics question, strong numeracy skills are fundamental in nursing for accurate medication dosage calculations, IV drip rate adjustments, and interpreting clinical data charts.
What if? If the question involved addition (1022 + 982), the difference of squares formula would not apply. One would have to calculate the squares directly (10404 + 9604 = 20008) or use other identities like (a+b)2 + (a-b)2 = 2(a2+b2).

How to Approach the Question

First, analyze the expression: 102 × 102 – 98 × 98.
Recognize that this expression is in the format of a2 - b2, which is a standard algebraic identity known as the 'difference of squares'.
Identify the values for 'a' and 'b'. In this case, a = 102 and b = 98.
Recall the formula for the difference of squares: a2 - b2 = (a - b)(a + b).
Substitute the values of 'a' and 'b' into the formula: (102 - 98) × (102 + 98).
Perform the calculations inside the parentheses: (4) × (200).

Concept Tested & Keywords

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