If $(2x - 5y)^3 - (2x + 5y)^3 = y[Ax^2 + By^2]$, then what is the value of $(2A - B)$?
Answer & explanation
Correct answer: option 4
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