`a)`
Ta có :
`(xz + yt)^2 + (xt - yz)^2`
` = (xz)^2 + 2 . xz . yt + (yt)^2 + (xt)^2 - 2 . xt . yz + (yz)^2`
` = x^2z^2 + 2xyt + y^2t^2 + x^2t^2 - 2xzyt + y^2z^2`
`= (x^2z^2+ x^2t^2) + (y^2z^2 + y^2t^2)`
` = x^2 (z^2 + t^2) + y^2 (z^2 + t^2)`
`= (x^2 + y^2)(z^2 + t^2)`
Vậy `(x^2 + y^2)(z^2 + t^2) = (xz + yt)^2 + (xt - yz)^2`
`b)`
Ta có :
`(x+y)^2 - (x-y)(x+y)`
` = (x^2 + y^2+ 2xy) - (x^2 - y^2)`
` = x^2 + y^2 + 2xy - x^2 + y^2`
` = 2y^2 + 2xy`
` = 2y (x + y)`
Vậy `(x+y)^2 - (x-y)(x+y) = 2y(x+y)`
