Question

设A=1-1/2x+3x²-x³，B=2（x³+x²-1/2x-1），

设A=1-1/2x+3x²-x³，B=2（x³+x²-1/2x-1），则1/2（A+B）-1/3(A-B)=_____（按x的降幂排列）

Answer 1

原式=A/2+B/2-A/3+B/3
=A/6+5B/6
=1/6(1-1/2x+3x²尺历-x³)-10(x³+x²-1/2x-1)/6
=1/6-1/12x+1/2x²型困段-1/6x³-5/3x³-5/卜誉3x²+5/6x+5/3
=-11/6x³-7/6x²+3/4x+3/2

Answer 2

设A=1-1/2x+3x²-x³，B=2（x³+x²-1/2x-1）穗搜，则1/2（A+B）-1/3(A-B)=6/2X³+13/6X²-11/12X-3/2
1/2（A+B）-1/3(A-B)
=1/2A+1/2B-1/3A+1/3B
=1/6A+5/6B
=1/6(1-1/2X+3X²-X³)+5/6(2X³+2X²-X-2)
=1/6-1/12X+1/2X²-1/6X³ +10/6X³键做+10/6X²-5/6X-10/6
=9/6X³猜亮历+13/6X²-11/12X-9/6
=6/2X³+13/6X²-11/12X-3/2

Answer 3

A=1-1/2x+3x²-x³埋誉
B=2（x³+x²-1/2x-1）
A+B得弯首段
1-1/2x+3x²-x³+2x³+2x²-x-2
=x³+5x²-3/2x-1
A-B
1-1/2x+3x²-x³-2x³-2x²+x+2
=-3x³+x²+1/2x+3

则1/2（A+B）-1/3(A-B)
=1/2(x³+5x²-3/2x-1)-1/3(-3x³+x²+1/2x+3)
=1/2x³+5/2x²-3/4x-1/2+x³芹姿-1/3x²-1/6x-1
=3/2x³+13/6x²-11/12x-3/2

Answer 4

(A+B)/2-(A-B)/3
=(A+5B)/友搭6
=(1-x/2+3x²-x³+10x³+10x²-5x-10)/棚告枯6
=(9x³链洞+13x²-11x/2-9)/6