Question

if
$x - y = - 2 \: and \: xy = 35 \: then \: \: {x}^{3} - {y}^{3} =$

Answer 1

Hello friend,
Here's your answer:

Answer = -218
In the pic, it went wrong a bit. 
Sorry for that 

Explantation = Refer the pic


Hope my answer helps you.

Answer 2

Here is the solution :

1st Equation : x-y = 2,
2nd Equation : xy = 35,

Simplifying 1st Eq,
=> y = x+2 --------- 3rd Equation,

Substituting 3rd Eq in 2nd Eq,

=> (x)(x+2) = 35,

=> x² + 2x = 35,

=> x² + 2x - 35 = 0,

=> x² + 7x - 5x - 35 = 0,

=> x(x+7) -5(x+7) = 0,

=> x-5 = 0, or x+7 = 0,

=> x = 5, or x = -7, Substituting these values in 1st Eq,

=> If x = 5 :
y = 5+2 = 7,

=> If x = -7,
y = -7+2 = -5,

=> x³ - y³ = either 5³ - 7³ or -7³ - (-5)³

=> x³ - y³ is always -218,

Therefore : x³ - y³ = -218

There is also another way to find !. But in this way, we can have x and y values too !..

Hope you understand, Have a Great day !..
Thanking you, Bunti 360 !..