[(3x + 5y)^2 – 60xy] \div [(3x – 5y)^2]
Simplify:
निम्नलिखित को सरल कीजिए:
$[(3x + 5y)^2 – 60xy] \div [(3x – 5y)^2]$
Detailed Solution & Logic
Correct Answer:
1
Given expression:
$[(3x + 5y)^2 - 60xy] \div [(3x - 5y)^2]$
Step 1: Expand $(3x + 5y)^2$
$ (3x + 5y)^2 = 9x^2 + 30xy + 25y^2 $
Numerator:
$ (9x^2 + 30xy + 25y^2) - 60xy = 9x^2 - 30xy + 25y^2 $
Step 2: Factorize the numerator
$ 9x^2 - 30xy + 25y^2 = (3x - 5y)^2 $
Step 3: Simplify the fraction
$ \frac{(3x - 5y)^2}{(3x - 5y)^2} = 1 $
✅ Answer: 1
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