Cho 2 đa thức: A ( x ) = 2 x^3 − 5 x^2 + x + 5 B ( x ) = 7 x^3 − 2 x + 1 . (a) Tính A ( x ) + B ( x ) (b) Tính A ( x ) − B ( x )
Giải thích
a) \[A(x) + B(x) = (2{x^3} - 5{x^2} + x + 5) + (7{x^3} - 2x + 1)\]
\[ = \left( {2{x^3} + 7{x^3}} \right) - 5{x^2} + \left( {x - 2x} \right) + \left( {5 + 1} \right)\]
\[ = 9{x^3} - 5{x^2} - x + 6\]
b) \[A(x) - B(x) = (2{x^3} - 5{x^2} + x + 5) - (7{x^3} - 2x + 1)\]
\[ = 2{x^3} - 5{x^2} + x + 5 - 7{x^3} + 2x - 1\]
\[ = \left( {2{x^3} - 7{x^3}} \right) - 5{x^2} + \left( {x + 2x} \right) + \left( {5 - 1} \right)\]
\[ = - 5{x^3} - 5{x^2} + 3x + 4\].