Q433
If (x + y)3 + 8(x - y)3 = (3x + Ay)(3x2 + Bxy + Cy2), then the value of A + B + C is:
A.
0
AnswerB.
4
C.
2
D.
3
Answer: Option A
Solution
Answer: Option A
Solution:
(x + y)3 + 8(x - y)3 = (3x + Ay)(3x2 + Bxy + Cy2)a3 + b3 = (a + b)(a2 - ab + b2)
a = (x + y)
b = 2(x - y)
(x + y)3 + 8(x - y)3 = (3x - y)(x2 + y2 + 2xy - 2x2 + 2y2 + 4x2 + 4y2 - 8xy)
(x + y)3 + 8(x - y)3 = (3x - y)(3x2 - 6xy + 7y2)
(3x + Ay)(3x2 + Bxy + Cy2) = (3x - y)(3x2 - 6xy + 7y2)
Compare
A = -1
B = -6
C = 7
A + B + C = -1 - 6 + 7 = 0