Question

What should be added to x³ + 3x²y + 3xy² + y³ to get x³ + y³?

Answer 1

In order to find the solution subtract x³ + 3x²y + 3xy² + y³ from x³ + y³

Required expression is x³ + y³ – (x³ + 3x²y + 3xy² + y³) = x³ + y³ – x³ – 3x²y – 3xy² – y³

On combining the like terms,

= x³ – x³ + y³ – y³ – 3x²y – 3xy²

= –3x²y – 3xy²

So, if we add –3x²y – 3xy² in x³ + 3x²y + 3xy² + y³, we get x³ + y³.