`a)`
`(x+y)^2+(x-y)^2`
`=x^2+2xy+y^2+x^2-2xy+y^2`
`=(x^2+x^2)+(2xy-2xy)+(y^2+y^2)`
`=2x^2+2y^2`
`=2(x^2+y^2)`
`b)`
`(m+n+p)(m^2+n^2+p^2-mn-np-mp)`
`=m^3+mn^2+p^2m-m^2n-mnp-m^2p+m^2n+n^3+p^2n-n^2m-n^2p-mnp+m^2p+n^2p+p^3-mnp-p^2n-p^2m`
`=m^3+n^3+p^3-3mnp`
