Question

Multiple Choice question :


If (x + y)³ - (x - y)³ - 6y(x² - y²) = ky²
then , k =
a) 1
b) 2
c) 4
d) 8

Support your answer with a detailed method proving so

Answer 1

HELLO DEAR,

(X+Y)³ - (X-Y)³ -6Y(X²-Y²)=KY²

=> X³+Y³ + 3XY(X+Y) - [ X³-Y³-3XY(X-Y)] - 6Y( X²-Y²) = KY²

=> X³ + Y³ - X³ + Y³ + 3X²Y + 3XY² + 3X²Y -3XY² - 6X²Y + 6Y³= KY²

=> 2Y³ + 6X²Y - 6X²Y + 6Y³ = KY²

=> 8y³ =ky²

=> k=8y



I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Given Equation is (x+y)^3 - (x-y)^3 - 6y(x^2 - y^2).

x^3 + 3x^2y + 3xy^2 + y^3 - (x^3 - 3x^2y+3xy^2 - y^3) - 6y(x^2-y^2)

x^3 + 3x^2y + 3xy^2 + y^3 - x^3 + 3x^2y - 3xy^2 + y^3 - 6x^2y + 6y^3

8y^3.

Now,

8y^3 = ky^2

8y = k.




Hope this helps!