If 27x3 - 64 y3 = (Ax + By) (Cx2 - Dy2 + 12xy), then the value of 4A + B + 3C + 2D is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 3.
27x3 - 64 y3 = (Ax + By) (Cx2 - Dy2 + 12xy)
(3x)3 - (4y)3 = (3x - 4y)(9x2 + 16y2 + 12xy)
(3x - 4y)(9x2 + 16y2 + 12xy) = (Ax + By) (Cx2 - Dy2 + 12xy)
On comparing we get,
A = 3 , B = -4 , C = 9 and D = -16.
4A + B + 3C + 2D
= 4 × 3 - 4 + 3 × 9 + 2 × -16
= 12 - 4 + 27 - 32
= 3.