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1. 计算:
(1)$-20-(-14)-|-18|-13$;
(2)$25÷5×(-\dfrac{1}{5})÷(-\dfrac{3}{4})$;
(3)$-(\dfrac{1}{4}-\dfrac{1}{2})+9×(\dfrac{1}{6}-\dfrac{3}{8})$;
(4)$-1^{4}-(1-0.5)×\dfrac{1}{3}×[3-(-3)^{2}]$.
(1)$-20-(-14)-|-18|-13$;
(2)$25÷5×(-\dfrac{1}{5})÷(-\dfrac{3}{4})$;
(3)$-(\dfrac{1}{4}-\dfrac{1}{2})+9×(\dfrac{1}{6}-\dfrac{3}{8})$;
(4)$-1^{4}-(1-0.5)×\dfrac{1}{3}×[3-(-3)^{2}]$.
答案
(1)-37 (2)$\dfrac{4}{3}$ (3)$-1\dfrac{5}{8}$ (4)0
2. 化简:
(1) $\frac{1}{6}(2x - 3y) - \frac{5}{6}(2y - 3x) + y$; (2) $(2x^2 - 5x + 2) - (x^2 - x - 2) - (x^2 - 3x + 2)$.
(1) $\frac{1}{6}(2x - 3y) - \frac{5}{6}(2y - 3x) + y$; (2) $(2x^2 - 5x + 2) - (x^2 - x - 2) - (x^2 - 3x + 2)$.
答案
(1)$\dfrac{17}{6}x-\dfrac{7}{6}y$ (2)$-x+2$
3. 先化简,再求值:
$3m^2n - [2mn^2 - 2(mn - \dfrac{3}{2}m^2n) + mn] + 3mn^2$,其中$m=\dfrac{1}{2},n=-2$.
$3m^2n - [2mn^2 - 2(mn - \dfrac{3}{2}m^2n) + mn] + 3mn^2$,其中$m=\dfrac{1}{2},n=-2$.
答案
原式化简为 $mn^2+mn$,代入 $m=\dfrac{1}{2},n=-2$ 得 $\dfrac{1}{2}×(-2)^2+\dfrac{1}{2}×(-2)=1$.
4. 一位同学做一道题:已知两个多项式$A,B$,计算$2A+B$,他误将“$2A+B$”看成“$A+2B$”,求得的结果为$9x^2 - 2x + 7$,已知$B=x^2 + 3x - 2$,求$2A+B$的正确答案.
答案
由题意得,$A=9x^2-2x+7-2(x^2+3x-2)=9x^2-2x+7-2x^2-6x+4=7x^2-8x+11$,所以 $2A+B=2(7x^2-8x+11)+x^2+3x-2=14x^2-16x+22+x^2+3x-2=15x^2-13x+20$.
