Question

The product of two numbers is x^4-y^4. If one of them is x-y find the other number.​

Answer 1

Answer:

Let the other number be z

(x^2)^2-(y^2)^2=(x-y) × z

(x^2+y^2)(x^2-y^2)=(x-y) ×z

:- w. k. t (x-y) (x+y) = x^2 - y^2

let's multiply both the sides by (x+y)

(x^2+y^2)(x^2-y^2) (x+y) = z{(x-y) (x+y)}

z = (x^2+y^2)(x^2-y^2)(x+y) / (x-y) (x+y)

z = (x^2+y^2)(x^2-y^2)(x+y) / x^2-y^2

Now, x^2-y^2 will get cancelled

z = (x^2+y^2)(x+y)

z = x^3+x^2y+y^2x+y^3

or

z = x^3+y^3+xy(x+y)

So, x^3+y^3+xy(x+y) is the other number

Hope it helps!