If $x^6 - 512 y^6 = (x^2 + Ay^2) (x^4 - Bx^2 y^2 + Cy^4)$, then what is the value of $(A + B - C)$?
Answer & explanation
Correct answer: option 1
x3 – y3 = (x – y) (x2 + xy + y2)
x6 – 512y6 = (x2 + Ay2)(x4 – Bx2y2 + Cy4)
[x2 – (√8 y)2] [x4 + 8 x2y2 + 64y4] = (x2 + Ay2) (x4 – Bx2y2 + Cy4)
Now, compare both the equations we get,
A = –8
B = –8
C = 64
Now,
(A + B – C) = (–8 – 8 – 64)
(A + B – C) = –80