17. 化简:
(1)$(4a^{2}b-2ab^{2})-2(ab^{2}-2a^{2}b)$;
(2)$3x^{2}-[7x-(4x-3)-2x^{2}]$.
答案:(1)8a²b-4ab²;(2)5x²-3x-3.
解析:
(1)$(4a^{2}b - 2ab^{2}) - 2(ab^{2} - 2a^{2}b)$
$=4a^{2}b - 2ab^{2} - 2ab^{2} + 4a^{2}b$
$=(4a^{2}b + 4a^{2}b) + (-2ab^{2} - 2ab^{2})$
$=8a^{2}b - 4ab^{2}$
(2)$3x^{2} - [7x - (4x - 3) - 2x^{2}]$
$=3x^{2} - (7x - 4x + 3 - 2x^{2})$
$=3x^{2} - 7x + 4x - 3 + 2x^{2}$
$=(3x^{2} + 2x^{2}) + (-7x + 4x) - 3$
$=5x^{2} - 3x - 3$
18. 已知$A= x^{3}+3$,$B= 2x^{3}-xy+2$.
(1)求$2A-B$;
(2)若$x$,$y$互为倒数,求$2A-B$的值.
答案:(1)xy+4;(2)5.
解析:
(1)因为$A = x^{3} + 3$,$B = 2x^{3}-xy + 2$,所以$2A - B=2(x^{3}+3)-(2x^{3}-xy + 2)=2x^{3}+6 - 2x^{3}+xy - 2=xy + 4$;
(2)因为$x$,$y$互为倒数,所以$xy = 1$,由(1)知$2A - B=xy + 4$,所以$2A - B=1 + 4=5$。
19. 先化简,再求值:
(1)$2(m^{2}+3mn)-4(m^{2}-2mn)-m^{2}$,其中$m= -1$,$n= \dfrac{1}{14}$;
(2)$3a^{2}b-\left \lbrack 2ab^{2}-2\left( ab-\dfrac{3}{2}a^{2}b\right)+ab\right\rbrack +3ab^{2}$,其中$a$,$b满足(a+3)^{2}+|b-1|= 0$.
答案:(1)原式化简为-3m²+14mn,值为-4;(2)原式化简为ab²+ab,值为-6.
解析:
(1)原式$=2m^{2}+6mn-4m^{2}+8mn-m^{2}$
$=(2m^{2}-4m^{2}-m^{2})+(6mn+8mn)$
$=-3m^{2}+14mn$
当$m=-1$,$n=\dfrac{1}{14}$时,
原式$=-3×(-1)^{2}+14×(-1)×\dfrac{1}{14}$
$=-3×1-1$
$=-3-1$
$=-4$
(2)原式$=3a^{2}b-[2ab^{2}-2ab+3a^{2}b+ab]+3ab^{2}$
$=3a^{2}b-[2ab^{2}-ab+3a^{2}b]+3ab^{2}$
$=3a^{2}b-2ab^{2}+ab-3a^{2}b+3ab^{2}$
$=(3a^{2}b-3a^{2}b)+(-2ab^{2}+3ab^{2})+ab$
$=ab^{2}+ab$
因为$(a+3)^{2}+|b-1|=0$,所以$a+3=0$,$b-1=0$,即$a=-3$,$b=1$
原式$=(-3)×1^{2}+(-3)×1$
$=-3-3$
$=-6$