Thu gọn đa thức sau: (a) M = y^2 - 2y + 1/2y^2 + 5y - y^2 (b) N = 1/3x^2y + xy^2 - xy + 1/2xy^2 - 5xy - 1/3x^2y

a) \(M = {y^2} - 2y + \frac{1}{2}{y^2} + 5y - {y^2}\)

\( = \left( {{y^2} + \frac{1}{2}{y^2} - {y^2}} \right) + \left( { - 2y + 5y} \right)\)

\( = \left( {1 + \frac{1}{2} + 1} \right){y^2} + \left( { - 2 + 5} \right)y\)

\( = \frac{1}{2}{y^2} + 3y\)

b) \(N = \frac{1}{3}{x^2}y + x{y^2} - xy + \frac{1}{2}x{y^2} - 5xy - \frac{1}{3}{x^2}y\)

\( = \left( {\frac{1}{3}{x^2}y - \frac{1}{3}{x^2}y} \right) + \left( {x{y^2} + \frac{1}{2}x{y^2}} \right) + \left( { - xy - 5xy} \right)\)

\( = 0 + \left( {1 + \frac{1}{2}} \right)x{y^2} + \left( { - 1 - 5} \right)xy\)

\( = \frac{3}{2}x{y^2} - 6xy\)