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75×75−2×75×25+25×25 is equal to:
10000
6250
7500
2500
2500
Recognize the identity a2−2ab+b2 where a=75 and b=25. The result is simply (75−25)2=502=2500.
Expression: 75 x 75 - 2 x 75 x 25 + 25 x 25
a2−2ab+b2=(a−b)2
Recognize the identity a2−2ab+b2 where a=75 and b=25. The result is simply (75−25)2=502=2500.
Multiplying the terms individually (5625−3750+625) is time-consuming and prone to calculation errors; always look for algebraic patterns first.
Identify algebraic identity
The expression follows the pattern a2−2ab+b2, where a=75 and b=25.
752−2(75)(25)+252
Apply the identity
Using the formula (a−b)2=a2−2ab+b2, we substitute a=75 and b=25.
(75−25)2
Calculate the result
Subtract the numbers inside the parentheses and square the result.
502=2500
D is correct because the expression simplifies to (75−25)2=502=2500.
This identity is fundamental in Quantitative Aptitude and appears frequently in simplifications involving large numbers, similar to problems involving (a+b)2 or (a2−b2).
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