Question

what should be added to x³ +3x²y + 3xy² + y³ to get x³ + y³​

Answer 1

Answer:

-3x(square)y and -3x y(square) should be added

Answer 2

Answer:

Let the polynomial to be added be M

According to question,

x

3

+3x

2

y+3xy

2

+y

3

+M=x

3

+y

3

⇒M=(x

3

+y

3

)−(x

3

+3x

2

y+3xy

2

+y

3

)

⇒M=x

3

+y

3

−x

3

−3x

2

y−3xy

2

−y

3

Collecting like terms,

⇒M=x

3

−x

3

+y

3

−y

3

−3x

2

y−3xy

2

⇒M=−3x

2

y−3xy

2

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