6. 已知 $A=3x^{2}-x+2y-4xy,B=2x^{2}-3x-y+xy.$
(1) 化简 $2A-3B.$
(2) 当 $x+y=\dfrac{6}{7},xy=-1$ 时,求 $2A-3B$ 的值.

(1)$2A - 3B = 2(3x^{2} - x + 2y - 4xy) - 3(2x^{2} - 3x - y + xy) = 6x^{2} - 2x + 4y - 8xy - 6x^{2} + 9x + 3y - 3xy = 7x + 7y - 11xy$.
(2)因为$x + y = \dfrac{6}{7},xy = -1$,所以$2A - 3B = 7x + 7y - 11xy = 7(x + y) - 11xy = 7×\dfrac{6}{7} - 11×(-1) = 6 + 11 = 17$.

7. 已知 $A=x^{3}+2x+3,B=2x^{3}-xy+2.$
(1)求 $2A-B.$
(2)若 $2A-B$ 的值与 $x$ 的取值无关,求 $y$ 的值.

(1)$2A - B = 2(x^{3} + 2x + 3) - (2x^{3} - xy + 2) = 2x^{3} + 4x + 6 - 2x^{3} + xy - 2 = xy + 4x + 4$.
(2)由(1),得$2A - B = xy + 4x + 4 = x(y + 4) + 4$.因为$2A - B$的值与$x$的取值无关,所以$y + 4 = 0$,解得$y = -4$.

8. 已知代数式 $A=3x^2-x+1$,马小虎同学在做整式加减运算时,误将“$A-B$”看成了“$A+B$”,得到的结果是 $2x^2-3x-2$.
(1)请你帮马小虎同学求出正确的结果.
(2)若 $x$ 是最大的负整数,将 $x$ 代入(1)中的结果求值.

(1)由题意,得$B = (A + B) - A = 2x^{2} - 3x - 2 - (3x^{2} - x + 1) = 2x^{2} - 3x - 2 - 3x^{2} + x - 1 = -x^{2} - 2x - 3$,所以$A - B = (3x^{2} - x + 1) - (-x^{2} - 2x - 3) = 3x^{2} - x + 1 + x^{2} + 2x + 3 = 4x^{2} + x + 4$.
(2)因为$x$是最大的负整数,所以$x = -1$,所以$A - B = 4x^{2} + x + 4 = 4×(-1)^{2} + (-1) + 4 = 4 - 1 + 4 = 7$.

9. 已知 $A=3a^{2}-4ab$ , $B=a^{2}+2ab$.
(1)求 $A-2B$.
(2)若 $|2a+1|+(2-b)^{2}=0$ ,求 $A-2B$ 的值.

(1)$A - 2B = (3a^{2} - 4ab) - 2(a^{2} + 2ab) = 3a^{2} - 4ab - 2a^{2} - 4ab = a^{2} - 8ab$.
(2)由题意,得$2a + 1 = 0,2 - b = 0$,所以$a = -\dfrac{1}{2},b = 2$,所以$A - 2B = (-\dfrac{1}{2})^{2} - 8×(-\dfrac{1}{2})×2 = \dfrac{1}{4} + 8 = \dfrac{33}{4}$.