3.利用因式分解计算:$(-2)^{101}+(-2)^{100}-(-2^{100}).$
答案：解:原式$=-2^{101}+2^{100}+2^{100}=2^{100}×(-2+1+1)=0.$
4.若$ab=7$，$a+b=6$，求多项式$a^2b+ab^2$的值.
答案：解:$\because ab=7,a+b=6,$
$\therefore a^2b+ab^2=ab(a+b)=7×6=42.$
$\therefore a^2b+ab^2=ab(a+b)=7×6=42.$
5.已知$6x - 3y - 1 = 0$，$xy = 2$，求$2x^4y^3 - x^3y^4$的值.
答案：解:$\because 6x-3y-1=0,\therefore 2x-y=\frac{1}{3},$
$\therefore 当2x-y=\frac{1}{3},xy=2时,$
原式$=(xy)^3·(2x-y)=2^3×\frac{1}{3}=\frac{8}{3}.$
$\therefore 当2x-y=\frac{1}{3},xy=2时,$
原式$=(xy)^3·(2x-y)=2^3×\frac{1}{3}=\frac{8}{3}.$