If (x + y)3 + 8 (x - y)3 = (3x + Ay)(3x2 + Bxy + Cy2), then the value of A + B + C is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 0
⇒ (x + y)3 + 8 (x - y)3
⇒ (x + y)3 + (2x - 2y)3
⇒ a3 + b3 = (a + b)(a2 + b2 - ab)
⇒ (x + y + 2x - 2y)[(x + y)2 + (2x - 2y)2 - (x + y)(2x - 2y)]
⇒(3x - y)[(x2 + y2 + 2xy + 4x2 + 4y2 - 8xy - 2x2 + 2xy - 2xy + 2y2]
⇒ (3x - y)[3x2 + 7y2 - 6xy] = (3x + Ay)(3x2 + Bxy + Cy2)
on comparing we get,
A = -1, B = -6 and C = 7
A + B + C = -1 - 6 + 7 = 0.