Question : If $27 x^{3} - 64 y^{3} = (A x + B y) (C x^{2} - D y^{2} + 12 x y)$ , then the value of $4 A + B + 3 C + 2 D$ is:
Option 1: 5
Option 2: 3
Option 3: –3
Option 4: –4

Question

Question : If $(x + y)^{3} + 8 (x - y)^{3} = (3 x + A y) (3 x^{2} + B x y + C y^{2})$ , then the value of (A + B + C) is:
Option 1: 0
Option 2: 4
Option 3: 2
Option 4: 3

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Answer 1

Correct Answer: 3

Solution : Given: $27 x^{3} - 64 y^{3} = (A x + B y) (C x^{2} - D y^{2} + 12 x y)$
⇒ $(3 x)^{3} - (4 y)^{3} = (A x + B y) (C x^{2} - D y^{2} + 12 x y)$
⇒ $(3 x - 4 y) (9 x^{2} + 16 y^{2} + 12 x y) = (A x + B y) (C x^{2} - D y^{2} + 12 x y)$
$∴$ 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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Question : If 27x3−64y3=(Ax+By)(Cx2−Dy2+12xy), then the value of 4A+B+3C+2D is:Option 1: 5Option 2: 3Option 3: –3Option 4: –4

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Question : If $27 x^{3} - 64 y^{3} = (A x + B y) (C x^{2} - D y^{2} + 12 x y)$ , then the value of $4 A + B + 3 C + 2 D$ is:
Option 1: 5
Option 2: 3
Option 3: –3
Option 4: –4