Nội dung bài giảng
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
Giải
\(\eqalign{
& {\rm{a}})M + N = ({x^2} - 2yz + {z^2}) + (3yz - {z^2} + 5{{\rm{x}}^2}) \cr
& = {x^2} - 2yz + {z^2} + 3yz - {z^2} + 5{{\rm{x}}^2} \cr
& = (1 + 5){x^2} + ( - 2 + 3)yz + (1 - 1){z^2} = 6{{\rm{x}}^2} + yz \cr} \)
b) \(M - N = ({x^2} - 2yz + {z^2}) - (3yz - {z^2} + 5{{\rm{x}}^2}) \)
\(= {x^2} - 2yz + {z^2} - 3yz + {z^2} - 5{{\rm{x}}^2}\)
\(= (1 - 5){x^2} - (2 + 3)yz + (1 + 1){z^2} \)
\(= - 4{{\rm{x}}^2} - 5yz + 2{{\rm{z}}^2}\)
\(N - M = (3yz - {z^2} + 5{{\rm{x}}^2}) - ({x^2} - 2yz + {z^2})\)
\(\eqalign{
& = 3yz - {z^2} + 5{{\rm{x}}^2} - {x^2} + 2yz - {z^2} \cr
& = (3 + 2)yz - (1 + 1){{\rm{z}}^2} + (5 - 1){x^2} \cr
& = 5yz - 2{{\rm{z}}^2} + 4{{\rm{x}}^2} \cr} \)