Question

$if (x + y) {}^{3} - (x - y) { }^{3} - 6y(x {}^{2} - y {}^{2} ) = ky {}^{3} \: then \: k =$

Answer 1

Let,

A = x + y,  B = x -y.

Now,

= ( A - B ) ^ 3

= A ^ 3 - B ^ 3 - 3AB ( A + B ) ------------------------ eq.1

Now, by putting the value of 'A' and 'B', in  eq.1

= ( x + y ) ^ 3 - ( x - y ) ^3 - 3 ( x + y ) ( x - y ) ( x + y - x + y )

= ( x + y ) ^ 3 - ( x - y ) ^ 3 - 3 * 2y ( x ^ 2 - y ^ 2 )

= ( x + y ) ^ 3 - ( x - y ) ^ 3 - 6y ( x ^ 2 - y ^ 2 )  =  ky^3

= ( x  + y - x + y ) ^ 3 = ky^3

= ( 2 y ) ^ 3  = ky^3

= 8 y ^ 3 = ky^3

k = 8 y ^ 3 / y ^ 3

k = 8.