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

Question

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

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Answer 1

Correct Answer: 0

Solution : $(x + y)^{3} + 8 (x - y)^{3} = (3 x + A y) (3 x^{2} + B x y + C y^{2})$
Taking L.H.S.
$(x + y)^{3} + 8 (x - y)^{3}$
$= (x + y)^{3} + [2 (x - y)]^{3}$
Using identity, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$
$= [x + y + 2 (x - y)] [(x + y)^{2} - 2 (x + y) (x - y) + [2 (x - y)]^{2}]$
$= (3 x - y) [(x^{2} + y^{2} + 2 x y) - 2 (x^{2} - y^{2}) + [4 (x^{2} + y^{2} - 2 x y]]$
$= (3 x - y) [x^{2} + y^{2} + 2 x y - 2 x^{2} + 2 y^{2} + 4 x^{2} + 4 y^{2} - 8 x y]$
$= (3 x - y) (3 x^{2} - 6 x y + 7 y^{2})$
On comparing the coefficient with R.H.S., we get,
⇒ A = –1
⇒ B = –6
⇒ C = 7
$∴$ (A + B + C) = – 1 – 6 + 7 = 0
Hence, the correct answer is 0.

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Question : If (x+y)3+8(x−y)3=(3x+Ay)(3x2+Bxy+Cy2), then the value of (A + B + C) is:Option 1: 0Option 2: 4Option 3: 2Option 4: 3

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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