先化简,再求值:
(1)$3(2a^{2}+5a-1)-4(3-8a-6a^{2})$,其中$a= -1$;
(2)$5(3a^{2}b-ab^{2})-(ab^{2}+3a^{2}b)$,其中$a= \frac {1}{2},b= \frac {1}{3}$;
(3)已知$|a-2|+(b+1)^{2}= 0$,求$5ab^{2}-[2a^{2}b-(4ab^{2}-2a^{2}b)]$的值;
(4)已知$a+b= 7,ab= 10$,求代数式$(5ab+4a+7b)+(6a-3ab)-(4ab-3b)$的值;
(5)已知$m^{2}+3mn= 5$,求$5m^{2}-[5m^{2}-(2m^{2}-mn)-7mn-5]$的值。
(1)$3(2a^{2}+5a-1)-4(3-8a-6a^{2})$,其中$a= -1$;
(2)$5(3a^{2}b-ab^{2})-(ab^{2}+3a^{2}b)$,其中$a= \frac {1}{2},b= \frac {1}{3}$;
(3)已知$|a-2|+(b+1)^{2}= 0$,求$5ab^{2}-[2a^{2}b-(4ab^{2}-2a^{2}b)]$的值;
(4)已知$a+b= 7,ab= 10$,求代数式$(5ab+4a+7b)+(6a-3ab)-(4ab-3b)$的值;
(5)已知$m^{2}+3mn= 5$,求$5m^{2}-[5m^{2}-(2m^{2}-mn)-7mn-5]$的值。
答案:(1)$30a^{2}+47a-15$,$-32$ (2)$12a^{2}b-6ab^{2}$,$\frac {2}{3}$ (3)$9ab^{2}-4a^{2}b$,34 (4)$10a+10b-2ab$,50 (5)$2m^{2}+6mn+5$,15
解析:
(1)解:原式$=6a^{2}+15a-3-12+32a+24a^{2}=(6a^{2}+24a^{2})+(15a+32a)+(-3-12)=30a^{2}+47a-15$
当$a=-1$时,原式$=30×(-1)^{2}+47×(-1)-15=30-47-15=-32$
(2)解:原式$=15a^{2}b-5ab^{2}-ab^{2}-3a^{2}b=(15a^{2}b-3a^{2}b)+(-5ab^{2}-ab^{2})=12a^{2}b-6ab^{2}$
当$a=\frac{1}{2},b=\frac{1}{3}$时,原式$=12×(\frac{1}{2})^{2}×\frac{1}{3}-6×\frac{1}{2}×(\frac{1}{3})^{2}=12×\frac{1}{4}×\frac{1}{3}-6×\frac{1}{2}×\frac{1}{9}=1-\frac{1}{3}=\frac{2}{3}$
(3)解:原式$=5ab^{2}-[2a^{2}b-4ab^{2}+2a^{2}b]=5ab^{2}-(4a^{2}b-4ab^{2})=5ab^{2}-4a^{2}b+4ab^{2}=9ab^{2}-4a^{2}b$
因为$|a-2|+(b+1)^{2}=0$,所以$a-2=0,b+1=0$,即$a=2,b=-1$
当$a=2,b=-1$时,原式$=9×2×(-1)^{2}-4×2^{2}×(-1)=18+16=34$
(4)解:原式$=5ab+4a+7b+6a-3ab-4ab+3b=(5ab-3ab-4ab)+(4a+6a)+(7b+3b)=-2ab+10a+10b=10a+10b-2ab$
当$a+b=7,ab=10$时,原式$=10(a+b)-2ab=10×7-2×10=70-20=50$
(5)解:原式$=5m^{2}-[5m^{2}-2m^{2}+mn-7mn-5]=5m^{2}-(3m^{2}-6mn-5)=5m^{2}-3m^{2}+6mn+5=2m^{2}+6mn+5$
当$m^{2}+3mn=5$时,原式$=2(m^{2}+3mn)+5=2×5+5=15$
当$a=-1$时,原式$=30×(-1)^{2}+47×(-1)-15=30-47-15=-32$
(2)解:原式$=15a^{2}b-5ab^{2}-ab^{2}-3a^{2}b=(15a^{2}b-3a^{2}b)+(-5ab^{2}-ab^{2})=12a^{2}b-6ab^{2}$
当$a=\frac{1}{2},b=\frac{1}{3}$时,原式$=12×(\frac{1}{2})^{2}×\frac{1}{3}-6×\frac{1}{2}×(\frac{1}{3})^{2}=12×\frac{1}{4}×\frac{1}{3}-6×\frac{1}{2}×\frac{1}{9}=1-\frac{1}{3}=\frac{2}{3}$
(3)解:原式$=5ab^{2}-[2a^{2}b-4ab^{2}+2a^{2}b]=5ab^{2}-(4a^{2}b-4ab^{2})=5ab^{2}-4a^{2}b+4ab^{2}=9ab^{2}-4a^{2}b$
因为$|a-2|+(b+1)^{2}=0$,所以$a-2=0,b+1=0$,即$a=2,b=-1$
当$a=2,b=-1$时,原式$=9×2×(-1)^{2}-4×2^{2}×(-1)=18+16=34$
(4)解:原式$=5ab+4a+7b+6a-3ab-4ab+3b=(5ab-3ab-4ab)+(4a+6a)+(7b+3b)=-2ab+10a+10b=10a+10b-2ab$
当$a+b=7,ab=10$时,原式$=10(a+b)-2ab=10×7-2×10=70-20=50$
(5)解:原式$=5m^{2}-[5m^{2}-2m^{2}+mn-7mn-5]=5m^{2}-(3m^{2}-6mn-5)=5m^{2}-3m^{2}+6mn+5=2m^{2}+6mn+5$
当$m^{2}+3mn=5$时,原式$=2(m^{2}+3mn)+5=2×5+5=15$