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Cho hai đa thức :
\(M = {x^2} – 2yz + {z^2}\)
\(N = 3yz – {z^2} + 5{{\rm{x}}^2}\)
a) Tính M + N
b) Tính M – N; N – M
\(\eqalign{
& {\rm{a}})M + N = ({x^2} – 2yz + {z^2}) + (3yz – {z^2} + 5{{\rm{x}}^2}) \cr
& = {x^2} – 2yz + {z^2} + 3yz – {z^2} + 5{{\rm{x}}^2} \cr
& = (1 + 5){x^2} + ( – 2 + 3)yz + (1 – 1){z^2} = 6{{\rm{x}}^2} + yz \cr} \)
b) \(M – N = ({x^2} – 2yz + {z^2}) – (3yz – {z^2} + 5{{\rm{x}}^2}) \)
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\(= {x^2} – 2yz + {z^2} – 3yz + {z^2} – 5{{\rm{x}}^2}\)
\(= (1 – 5){x^2} – (2 + 3)yz + (1 + 1){z^2} \)
\(= – 4{{\rm{x}}^2} – 5yz + 2{{\rm{z}}^2}\)
\(N – M = (3yz – {z^2} + 5{{\rm{x}}^2}) – ({x^2} – 2yz + {z^2})\)
\(\eqalign{
& = 3yz – {z^2} + 5{{\rm{x}}^2} – {x^2} + 2yz – {z^2} \cr
& = (3 + 2)yz – (1 + 1){{\rm{z}}^2} + (5 – 1){x^2} \cr
& = 5yz – 2{{\rm{z}}^2} + 4{{\rm{x}}^2} \cr} \)