a/

31.64+7.30+146.31=31.(64+146)+7.30

=31.210+7.30=6510+210=6720

b/2³.3².28+2³.3⁵.8=2³.(3².28+3⁵.8)

=2³.(9.28+243.8)=8.(252+1944)

=8.2196=17568

c) Ta có: x+11 chia hết cho x+1

x+1+10 chia hết cho x+1

Vì x+1 chia hết cho x+1 nên 10 chia hết cho x+1.

Vậy x+1\(\inƯ\left(10\right)=\left\{1;2;5;10\right\}\)

\(\Rightarrow x\in\left\{0;1;4;9\right\}\)

\(25.2^3+75.2^3=2^3.\left(25+75\right)=8.100=800\)

\(3^2.187-87.3^2=3^2.\left(187-87\right)=9.100=900\)

\(4^2.19+80.4^2+4^2=4^2\left(19+80+1\right)=16.100=1600\)

\(73.5^2+5^2.28-5^2=5^2\left(73+28-1\right)=25.100=2500\)

\(6^2.48+51.6^2+36=6^2\left(48+51+1\right)=36.100=3600\)

\(113.7^2-7^2.12-49=49.\left(113-12-1\right)=4900\)

a. 25.2³ + 75.2³

= 2³(25 + 75)

= 8 . 100

= 800

b. 3² . 187 - 87.3² 

= 3² . (187 - 87)

= 9 . 100

= 900

c. 4² . 19 + 80 . 4² + 4²

= 4² . (19 + 80 + 1)

= 16 . 100

= 1600

d. 73 . 5² + 5². 28 - 5²

= 5² . (73 + 28 - 1)

= 25 . 100

= 2500

e. 6² . 48 + 51 . 6² + 36

= 36 . 48 + 51 . 36 + 36

= 36 . (48 + 51 + 1)

= 36 . 100

= 3600

g. 113.7² - 7².12 - 49

= 113 . 49 - 49 . 12 - 49

= 49. (113 - 12 - 1)

= 49 . 100

= 4900

j. (2³ . 9⁴ + 9³ . 45) : (9² . 10 - 9²)

= (2³ . 9⁴ + 9³ . 9.5) : [9²(10 - 1)]

= [9. (2³ . 9³ + 9² . 9.5)] : (9² . 9)

= {9. [9² (2³ + 9.5)]} : (9² . 9)

= (9. 9² . 53): 9³

= 9³ . 53 : 9³

= (9³:9³) . 53

= 53

a, 25 . 2³ + 75 . 2³ 
 = 2³ . (25 + 75)
 = 8 . 100
 = 800
b, 3² . 187 - 87. 3² 
 = 3² . (187 - 87)
 = 27 . 100
 = 2700
c, 4² . 19 + 80. 4² + 4² 
 = 4² . (19 + 80 +1)
 = 16 . 100
 = 1600
d, 73 . 5² + 5² . 28 - 5² 
 = 5² . (73 + 28 - 1)
 = 25 . 100
 = 2500
e, 6² .48 + 51. 6² + 36
 = 6² .48 + 51. 6² + 6² 
 = 6² . (48 + 51 + 1)
 = 36 . 100
 = 3600
g, 113. 7² - 7² .12 - 49
 = 113. 7² - 7² . 12 - 7² 
 = 7² . (113 - 12 - 1)
 = 49 . 100
 = 4900
h, (2³ . 9⁴ + 9³ .45): (9² .10 - 9² )
 = (8 . 9⁴ + 9³ . 9.5) : [9² .(10 - 1)]
 = (8 . 9⁴ + 9⁴ .5) : (9² . 9)
 = [9⁴ . (8 + 5)] : 9³ 
 =(6561 . 13) : 729
 = 85293 : 729
 = 117
Chúc bạn học tốt

\(A=\frac{3^2}{2.5}+\frac{3^2}{5.8}+\frac{3^2}{8.11}=3.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}\right)\)

\(=3.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}\right)=3.\left(\frac{1}{2}-\frac{1}{11}\right)\)

\(=3.\left(\frac{11}{22}-\frac{2}{22}\right)=3.\frac{9}{22}=\frac{27}{22}\)

1320 ta

a) 3.5² - 162:3⁴ + 3.3² = 3.5² - 2 + 3³ = 73 + 27 = 100        

3/2.5 + ...+ 3/17 .20

= 3/2 .(1/2 - 1/5 + 1/5 - 1/8 + ... + 1/17 - 120)

= 3/2 . (1/2 - 1/20)

= \(\frac{3}{2}\) . \(\frac{9}{20}\) = \(\frac{27}{40}\)

P= 3/ 2.5 + 3/5.8 + 3/8.11 + .... + 3/17.20

P= 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + .... + 1 /17 - 1/20

P= 1 / 2 - 1 / 20

P = 9/20

\(P=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{17.20}\)

\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\)

\(\frac{9}{20}\)