Question

(x+y)\(^3\)+(x-y)\(^3\)

Answer 1

`(x+y)^3 +(x-y)^3 `

`=[(x+y)+(x-y)][(x+y)^2 -(x+y)(x-y)+(x-y)^2 ]`

`=(x+y+x-y)[x^2 +2xy+y^2 -(x^2 -y^2 )+x^2 -2xy+y^2 ]`

`=2x(2x^2 +2y^2 -x^2 +y^2 )`

`=2x(x^2 +3y^2 )`

`=2x^3 +6xy^2`

Answer 2

\(\left(x+y\right)^3+\left(x-y\right)^3\)

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

\(=2x^3+6x^2y+2y^3\) 

\(=2xy\left(x^2+3x^2+y^2\right)\)