a) x⁵-3x²+x⁴-\(\dfrac{1}{2}\)x-x⁵+5x⁴+x²-1

= (x⁵-x⁵)+(x⁴+5x⁴)+(x²-3x²)-\(\dfrac{1}{2}\)x-1

= 6x⁴-2x²-\(\dfrac{1}{2}\)x-1

b) x-x⁹+x²-5x³+x⁶-x+3x⁹+2x⁶-x³+7

= (3x⁹-x⁹)+(2x⁶+x⁶)-(5x³+x³)+x²+(x-x)+7

= 2x⁹+3x⁶-6x³+x²+7

a) f(x) = -15x³+5x⁴-4x²+8x²-9x³-x⁴+15-7x³

= (5x⁴-x⁴)-(15x³+9x³+7x³)+(8x²-4x²)+15

= 4x⁴-31x³+4x²+15

b) f(1)= 4.1⁴-31.1³+4.1²+15 = -8

f(-1) = 4.(-1)⁴-31.(-1)³+4.(-1)²+15 = 54

a) xyz - 5xyz = -4xyz

b) x² - \(\dfrac{1}{2}\)x² - 2x² = -\(\dfrac{3}{2}\)x²

a) 2x²yz + 4xy²z - 5x²yz + xy²z - xyz

= (2x²yz-5x²yz)+(4xy²z+xy²z)-xyz

= -3x²yz + 5xy²z - xyz

b) x³-5xy+3x³+xy-x²+\(\dfrac{1}{2}\)xy-x²

= (x³+3x³)+(xy-5xy+\(\dfrac{1}{2}\)xy)-(x²+x²)

= 4x³-\(\dfrac{7}{2}\)xy-2x²

a) x⁶+x²y⁵+xy⁶+x²y⁵-xy⁶

= x⁶+(x²y⁵+x²y⁵)+(xy⁶-xy⁶)

= x⁶+2x²y⁵

b) \(\dfrac{1}{2}\)x²y³-x²y³+3x²y²z²-z⁴-3x²y²z²

= (\(\dfrac{1}{2}\)x²y³-x²y³)+(3x²y²z²-3x²y²z²)-z⁴

= -\(\dfrac{1}{2}\)x²y³-z⁴