If $(2x - 5y)^3 - (2x + 5y)^3 = y[Ax^2 + By^2]$, then what is the value of $(2A - B)$?

10

a³ – b³ = (a – b) (a² + b² + ab)

 (2x – 5x)³ – (2x + 5y)³ = y[Ax² + By²]

= [(2x – 5y) – (2x + 5y)] [(2x – 5y)² + (2x + 5y)² + (2x – 5y)(2x + 5y)] = y[Ax² + By²]

= [2x – 5y – 2x – 5y][4x² + 25y² – 20xy + 4x² + 25y² + 20xy + 4x² – 25y²] = y[Ax² + By²]

= [ – 10y] [12x² + 25y²] = y[Ax² + By²]

= y [ – 120x² – 250y²] = y[Ax² + By²]

On comparing

= A = – 120 and B = – 250

Now,

= (2A – B)

= [2 × ( – 120)] – ( – 250) = – 240 + 250

= 10