If `a/b = x/y`, then show that ` (a+b) (a^(2)+b^(2))x^(3) = (x+y)(x^(2)+y^(2))a^(3)`

Explanation

`a/b = x/y = k " (let)" [k ne 0]`
` :. A = bk " and " x = yk`.
Now, LHS ` = (a + b)(a^(2)+b^(2)) x^(3)`
` = (bk+b){(bk)^(2) +b^(2)}. (yk)^(3)`
` = b (k+1).b^(2)(k^(2)+1).y^(3)k^(3)`
` = b^(3)(k+1)(k^(2)+1).y^(3) k^(3)`.
RHS ` = (x+y)(x^(2)+y^(2)) a^(3)`
` = (yk+y){(yk)^(2) + y^(2)}. (bk)^(3)`
` = y (k+1_.y^(2) (k^(2)+1). b^(3)k^(3)`
` = y^(3) (k+1)(k^(2)+1) . b^(3)k^(3)`
` = b^(3)(k+1) (k^(2)+1) . y^(3) k^(3)`.
` :. ` LHS = RHS