Question : If $(2x - 5y)^3 - (2x+5y)^3 = y[Ax^2 + By^2]$, then what is the value of $(2A - B)$?
Option 1: 25
Option 2: 10
Option 3: 15
Option 4: 40
Correct Answer: 10
Solution :
According to the question,
$(2x - 5y)^3 - (2x+5y)^3 = y[Ax^2 + By^2]$
⇒ $[2x - 5y - 2x - 5y][4x^{2} + 25y^{2} + 20 xy + 4x^{2} - 25y^{2}] = y[Ax^{2} + By^{2}]$
⇒ $[-10y] [ 12x^{2} + 25y^{2}] = y[Ax^{2} + By^{2}]$
⇒ $y[ -120x^{2} - 250y^{2}] = y[Ax^{2} + By^{2}]$
Comparing both sides, we get,
$A = –120, B = –250$
Now,
⇒ $(2A - B) = - 240 + 250 = 10$
Hence, the correct answer is 10.
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