a) (3x² + y + xy + 3/2 .2x².txy + x²)
= 3x² + x² + y + xy + 3x³yt
= 4x² + y + xy + 3x³yt
b) xy + 3xy + x² + y³ + x² + t
= (xy + 3xy) + (x² + x²) + y³ + t
= 4xy + 2x² + y³ + t
c) 8x - x³ + x² + y² + 1/2y² + 3x - 4x³ + y³ + 8xy
= (-x³ - 4x³) + x² + (8x + 3x) + y³ + (y² + 1/2 y²) + 8xy
= -5x³ + x² + 11x + y³ + 3/2y² + 8xy
d) 1/2x²y + xy² - xy + 1/2xy² - 5xy - 1/3x²y
= (1/2x²y - 1/3x²y) + (xy² + 1/2xy²) + (-xy - 5xy)
= 1/6x²y + 3/2xy² - 6xy
e) 3x²y + 1/4xy + 1 - 3x²y + 1/2xy - 1/4xy
= (3x²y - 3x²y) + (1/4xy - 1/4xy + 1/2xy) + 1
= 1/2xy + 1
f) 5x²yz + 8xyz² - 3x²yz - xyz + x²yz + xyz²
= (5x²yz - 3x²yz + x²yz) + (8xyz² + xyz²) - xyz
= 3x²yz + 9xyz² - xyz
