Question : If x6 – 512y6 = (x2 + Ay2) (x4 – Bx2 y2 + Cy4), then what is the value of (A + B – C)?
Option 1: –80
Option 2: –72
Option 3: 72
Option 4: 48
Correct Answer: –80
Solution :
Given: $ x^6 - 512y^6 = (x^2 + Ay^2)(x^4 - Bx^2y^2 + Cy^4)$
$\Rightarrow \left \{ x^2 - (\sqrt{8}y)^2 \right \}\left \{ x^4 + 8x^2y^2 + 64y^4 \right \} = (x^2 + Ay^2)(x^4 - Bx^2y^2 + Cy^4)$
On comparing, we get,
A = –8, B = –8 and C = 64
$\therefore$ (A + B – C) = ( –8 – 8 – 64) = –80
Hence, the correct answer is –80.
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