Question

If (x+y)^3-(x-y)^3-6y(x^2-y^2)=ky^2, find k

Answer 1

x + y)³ -( x -y)³ -6y(x² - y² ) = Ky²

we know,
a³ - b³ = (a - b)( a² + ab + b²)

(x + y)³ -(x - y)³ = (x + y - x + y){(x +y)² + ( x -y)² + (x +y)(x -y) }

=( 2y ) { 2x² + 2y² + x² - y²)

= 2y ( 3x² + y²)

put this in above ,

2y ( 3x² + y²) -6y( x² - y²) = Ky²

6x²y +2y³ -6x²y +6y³ = Ky²

8y³ = Ky²

K = 8y