c) (\(\dfrac{1}{2}\)xy\(^2\) + x\(^2\) - x\(^2\)y) - M = -xy\(^2\) + x\(^2\)y + 1

=> M = (\(\dfrac{1}{2}\)xy\(^2\) + x\(^2\) - x\(^2\)y) - (-xy\(^2\) + x\(^2\)y + 1)

M = \(\dfrac{1}{2}\)xy\(^2\) + x\(^2\) - x\(^2\)y + xy\(^2\) - x\(^2\)y - 1

M = (\(\dfrac{1}{2}\)xy\(^2\) + xy\(^2\)) + (-x\(^2\)y - x\(^2\)y) + x\(^2\) - 1

M = \(\dfrac{3}{2}\)xy\(^2\) - 2x\(^2\)y + x\(^2\) - 1

b) M + (3x\(^2\)y - 2xy\(^3\)) = 2x\(^2\)y - 4xy\(^3\)

=> M = (2x\(^2\)y - 4xy\(^3\)) - (3x\(^2\)y - 2xy\(^3\))

M = 2x\(^2\)y - 4xy\(^3\) - 3x\(^2\)y + 2xy\(^3\)

M = (2x\(^2\)y - 3x\(^2\)y) + (-4xy\(^3\) + 2xy\(^3\))

M = -1x\(^2\)y - 2xy\(^3\)

Vậy đa thức M = -1x\(^2\)y - 2xy\(^3\)

a) M + (5x\(^2\) - 2xy) = 6x\(^2\) + 9xy - y\(^2\)

=> M = (6x\(^2\) + 9xy - y\(^2\)) - (5x\(^2\) - 2xy)

M = 6x\(^2\) + 9xy - y\(^2\) - 5x\(^2\) + 2xy

M = (6x\(^2\) - 5x\(^2\)) + (9xy + 2xy) - y\(^2\)

M = 1x\(^2\) + 11xy - y\(^2\)