1.

Verify : (i) `x^3+y^3=(x+y)(x^2-x y+y^2)` (ii) `x^3-y^3=(x-y)(x^2+x y+y^2)`

Answer» (i) RHS= `(x+y)(x^2-xy+y^2)`
`= x(x^2-xy+y^2) + y(x^2-xy+y^2)`
`= x^3 cancel(- x^2y) + cancel(xy^2) + cancel(yx^2) cancel(- xy^2)+y^3`
`=x^3 + y^3` = LHS
hence proved
(ii) RHS = `(x-y)(x^2+xy+y^2)`
`= x(x^2+xy+y^2) - y(x^2+xy+y^2)`
`=x^3 +cancel(x^2y)+cancel(xy^2) cancel( - yx^2) cancel(-xy^2 )- y^3`
`=x^3- y^3` =LHS
hence proved


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