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UPSC Exam  >  UPSC Questions  >   If (2x − 5y)3 − (2x + 5y)3 = y [Ax2 + By2] .... Start Learning for Free
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If (2x − 5y)3 − (2x + 5y)3 = y [Ax2 + By2] . then what is the value of (2A − B)?
  • a)
    25
  • b)
    10
  • c)
    15
  • d)
    40
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If (2x − 5y)3 − (2x + 5y)3 = y [Ax2 + By2] . then what is the value o...
We know that:
(a + b)3 = a3 + b3 + 3a2b + 3ab2
and (a − b)3 = a3 − b3 − 3a2b + 3ab2⇒ (2x − 5y)3 − (2x +5y)3Expanding this term with these formulas:
a3 − b3 − 3a2b + 3ab2 − [a3 + b3 + 3a2b +3ab2]
= −2b3 − 6a2b
b [−2b2 − 6a2]
Now b = 5y and a = 2x
5y [−2y (25y2) − 24x2] = 5y [−50y2 − 24x2]
Comparing it with given equation: y [Ax2 + By2]
A = −120 and B = −250
2A − B = 2(−120) + 250 = 10
Hence the correct option is (b)
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If (2x − 5y)3 − (2x + 5y)3 = y [Ax2 + By2] . then what is the value of (2A − B)?a)25b)10c)15d)40Correct answer is option 'B'. Can you explain this answer?
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