Question

x^3 +y^3=(x+y)(x^2-xy^2+y^2)

​

Answer 1

Given, x

3

+y

3

=(x+y)(x

2

−xy+y

2

)

First take R.H.S

(x+y)(x

2

−xy+y

2

)

To multiply two polynomials, we multiply each monomial of one polynomial (with its sign) by each monomial (with its sign) of the other polynomial.

= x.x

2

−x

2

y+x.y

2

+y.x

2

−x.y

2

+y.y

2

= x

3

−x

2

y+xy

2

+x

2

y−xy

2

+y

3

= x

3

+y

3

So, L.H.S = R.H.S

x

3

+y

3

=x

3

+y

3

Hence, x

3

+y

3

=(x+y)(x

2

−xy+y

2

) is derived.