\( {\rm{a}})M + N = ({x^2} - 2yz + {z^2}) \)\(+ (3yz - {z^2} + 5{{\rm{x}}^2}) \)
\( = {x^2} - 2yz + {z^2} + 3yz - {z^2} + 5{{\rm{x}}^2} \)
\(=(x^2+5x^2)+(-2yz+3yz)\)\(+(z^2-z^2)\)
\( = (1 + 5){x^2} + ( - 2 + 3)yz + (1 - 1){z^2} \)
\(= 6{{\rm{x}}^2} + yz \)
b) +) \(M - N = ({x^2} - 2yz + {z^2}) \)\(- (3yz - {z^2} + 5{{\rm{x}}^2}) \)
\(= {x^2} - 2yz + {z^2} - 3yz + {z^2} - 5{{\rm{x}}^2}\)
\(=(x^2-5x^2)-(2yz+3yz)\)\(+(z^2+z^2)\)
\(= (1 - 5){x^2} - (2 + 3)yz + (1 + 1){z^2} \)
\(= - 4{{\rm{x}}^2} - 5yz + 2{{\rm{z}}^2}\)
+) \(N - M = (3yz - {z^2} + 5{{\rm{x}}^2}) \)\(- ({x^2} - 2yz + {z^2})\)
\( = 3yz - {z^2} + 5{{\rm{x}}^2} - {x^2} + 2yz - {z^2} \)
\(=(3yz+2yz)-(z^2+z^2)+(5x^2-x^2)\)
\( = (3 + 2)yz - (1 + 1){{\rm{z}}^2} + (5 - 1){x^2} \)
\( = 5yz - 2{{\rm{z}}^2} + 4{{\rm{x}}^2} \)
