Question

Với ba đa thức: \(A = {x^2} - 2{\rm{x}}y + {y^2};B = 2{{\rm{x}}^2} - {y^2};C = {x^2} - 3{\rm{x}}y\)(ở trong ví dụ 3). Hãy tính:

a) B – C

b) (B – C) + A

Answer 1

a) Ta có:

\(\begin{array}{l}B - C = \left( {2{{\rm{x}}^2} - {y^2}} \right) - \left( {{x^2} - 3{\rm{x}}y} \right)\\B - C = 2{{\rm{x}}^2} - {y^2} - {x^2} + 3{\rm{x}}y\\B - C = \left( {2{{\rm{x}}^2} - {x^2}} \right) + 3{\rm{x}}y - {y^2} = {x^2} + 3{\rm{x}}y - {y^2}\end{array}\)

b) Ta có: 

\(\begin{array}{l}(B - C) + A = {\rm{[}}\left( {2{{\rm{x}}^2} - {y^2}} \right) - \left( {{x^2} - 3{\rm{x}}y} \right){\rm{] + (}}{{\rm{x}}^2} - 2{\rm{x}}y + {y^2})\\(B - C) + A = {x^2} + 3{\rm{x}}y - {y^2} + {x^2} - 2{\rm{x}}y + {y^2}\\(B - C) + A = \left( {{x^2} + {x^2}} \right) + \left( {3{\rm{x}}y - 2{\rm{x}}y} \right) + \left( {{y^2} - {y^2}} \right)\\(B - C) + A = 2{{\rm{x}}^2} + xy\end{array}\)