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1. 计算:
(1) $3.5×\frac{3}{5}-(2-1.25)$;
(2) $48÷[(-2)^3-(-4)]-2$;
(3) $\frac{9}{8}×(\frac{1}{2}-\frac{1}{6})÷(-\frac{3}{4})-\frac{1}{8}$;
(4) $[1-(1-4^3×0.25^2)]×|2-(-3)^2|$.
(1) $3.5×\frac{3}{5}-(2-1.25)$;
(2) $48÷[(-2)^3-(-4)]-2$;
(3) $\frac{9}{8}×(\frac{1}{2}-\frac{1}{6})÷(-\frac{3}{4})-\frac{1}{8}$;
(4) $[1-(1-4^3×0.25^2)]×|2-(-3)^2|$.
答案
(1)1.35
(2)-14
(3)$-\frac{5}{8}$
(4)28
(2)-14
(3)$-\frac{5}{8}$
(4)28
2. 化简:
(1) $15x^2y - 12xy^2 + 13xy^2 - 16x^2y$; (2) $(3x^2 - 4) + (2x^2 - 5x + 6) - 2(x^2 - 5x)$.
(1) $15x^2y - 12xy^2 + 13xy^2 - 16x^2y$; (2) $(3x^2 - 4) + (2x^2 - 5x + 6) - 2(x^2 - 5x)$.
答案
(1)$-x^2y+xy^2$
(2)$3x^2+5x+2$
(2)$3x^2+5x+2$
3. 先化简,再求值:
$2x-\{ -3y+[3x-2(3x-y)]\}$,其中$x=-1,y=-\dfrac{1}{5}$.
$2x-\{ -3y+[3x-2(3x-y)]\}$,其中$x=-1,y=-\dfrac{1}{5}$.
答案
$2x-\{-3y+[3x-2(3x-y)]\} = 2x-[-3y+(3x-6x+2y)] = 2x-(-3y+3x-6x+2y) = 2x-(-y-3x) = 2x+y+3x = 5x+y$, 当$x = -1, y=-\frac{1}{5}$时, 原式$= 5×(-1) + (-\frac{1}{5}) = -\frac{26}{5}$.
4. 已知关于 $ x $ 的多项式 $(a+b)x^5+(b-2)x^3-2(a-1)x^2-2ax-3$ 中不含 $ x^3 $ 和 $ x^2 $ 项,试求当 $ x=-1 $ 时,这个多项式的值.
答案
由题意可知$b-2=0,-2(a-1)=0$,解得$b=2,a=1$,当$a=1,b=2$时,原多项式可化简为$3x^5-2x-3$,把$x=-1$代入,原式$=3x^5-2x-3=3×(-1)^5-2×(-1)-3=-3+2-3=-4$.
