Question

hello friends please tell me how to solve this problem​

Answer 1

Answer:

First symplify the equation in the left side using dedicated formulae. Then Compare the number attached with y² and You got it

Answer 2

Answer:

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

In this example after solving y^2 term is not remain.

Step-by-step explanation:

Formulas

$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\\(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$

So

$(x+y)^3 - (x -y)^3 - 6y (x^2 - y^2)\\ =[x^3 + 3x^2y + 3xy^2 + y^3]- [x^3 -3x^2y + 3xy^2 - y^3] -6y(x^2) - 6y(-y^2)\\= x^3 + 3x^2y + 3xy^2 + y^3- x^3 +3x^2y - 3xy^2 + y^3- 6yx^2 + 6y^3\\ =3x^2y + y^3 +3x^2y + y^3- 6yx^2 + 6y^3\\=6x^2y - 6yx^2 + 3y^3 + 6y^3\\= 9y^3$