`a)`
`x^2 + y^2`
`= -(x^2 - y^2)`
`= -[(x - y)(x + y)]`
`= -(x^2 + xy - xy - y^2)`
`= -(x^2 - y^2 + 2xy - 2xy)`
`= (x^2 + 2xy + y^2) - 2xy`
`= (x + y)^2 - 2xy`
`=> x^2 + y^2 = (x + y)^2 - 2xy` `(đpcm)`
`b)`
`(x^(n + 3) - x^(n + 1) . y^2) : (x + y)`
`= x^(n + 1) . (x^2 - y^2) : (x + y)`
`= x^(n + 1) . (x - y) . (x + y) : (x + y)`
`= x^(n + 1) . (x - y)`
`= x^(n + 2) - x^(n + 1) . y`
`=> (x^(n + 3) - x^(n + 1) . y^2) : (x + y) = x^(n + 2) - x^(n + 1) . y` `(đpcm)`