Tìm đa thức A, D biết: (a) A+x^2(x+1)=x(x+2)+(x^3−2x+2).

a) \(A + {x^2}\left( {x + 1} \right) = x\left( {x + 2} \right) + \left( {{x^3} - 2x + 2} \right)\)

\(A = x\left( {x + 2} \right) + \left( {{x^3} - 2x + 2} \right) - {x^2}\left( {x + 1} \right)\)

\(A = {x^2} + 2x + {x^3} - 2x + 2 - {x^3} - {x^2}\)

\(A = 2\)

Vậy \(A = 2\) .

b) \(3a{b^2} - {b^2} - D = - {b^2} + 2a{b^2} - 5\).

\(D = 3a{b^2} - {b^2} - \left( { - {b^2} + 2a{b^2} - 5} \right)\)

\(D = 3a{b^2} - {b^2} + {b^2} - 2a{b^2} + 5\)

\(D = a{b^2} + 5\)

Vậy \(D = a{b^2} + 5\).