Question : If $27 x^3-64 y^3=(A x+B y)\left(C x^2-D y^2+12 x y\right)$, then the value of $4 A+B+3 C+2 D$ is:
Option 1: 5
Option 2: 3
Option 3: –3
Option 4: –4
Correct Answer: 3
Solution :
Given: $27x^3 - 64y^3 = (Ax + By) (Cx^2 - Dy^2 + 12 xy)$
⇒ $(3x)^3 - (4y)^3=(Ax + By) (Cx^2 - Dy^2 + 12 xy)$
⇒ $(3x - 4y) (9x^2 + 16y^2 + 12 xy)=(Ax + By) (Cx^2 - Dy^2 + 12 xy)$
$\therefore$ A = 3, B = –4, C = 9, D = –16
Now, 4A + B + 3C + 2D
= 4 × 3 – 4 + 3 × 9 + 2 × (–16)
= 12 – 4 + 27 – 32
= 3
Hence, the correct answer is 3.
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