expand x^3+y^3

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

So,` x^3+y^3=(x+y)^3-3x^2y-3xy^2`

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

`=(x+y){(x+y)^2-3xy}`

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

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

**Therefore**, `x^3+y^3=(x+y)(x^2-xy+y^2)`

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