a: \(61\cdot45+61\cdot23-68\cdot51\)

\(=61\left(45+23\right)-68\cdot51\)

\(=68\cdot61-68\cdot51\)

\(=68\left(61-51\right)=68\cdot10=680\)

b: \(3\cdot5^2-\left(75-4\cdot2^3\right)\)

\(=75-75+4\cdot8\)

\(=4\cdot8=32\)

c: \(36:\left\{2^2\cdot5-\left[30-\left(5-1\right)^2\right]\right\}\)

\(=\dfrac{36}{20-30+4^2}\)

\(=\dfrac{36}{-10+16}=\dfrac{36}{6}=6\)

d: \(\left(12\cdot49-3\cdot2^2\cdot7^2\right):\left(2020\cdot2021\right)\)

\(=\dfrac{\left(12\cdot49-12\cdot49\right)}{2020\cdot2021}=0\)

Bài 2:

a: \(17-x=3\)

=>\(x=17-3\)

=>x=14(nhận)

b: \(2\cdot\left(x-1\right):3=6\)

=>\(2\left(x-1\right)=6\cdot3=18\)

=>x-1=18/2=9

=>x=9+1=10(nhận)

c: \(x+\left(-2\right)=\left(-11\right)+7\)

=>\(x-2=-4\)

=>\(x=-4+2=-2\left(loại\right)\)

d: \(\left(x-1\right)^2-5=20\)

=>\(\left(x-1\right)^2=25\)

=>\(\left[{}\begin{matrix}x-1=5\\x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\left(nhận\right)\\x=-4\left(loại\right)\end{matrix}\right.\)

Câu 3:

a: Đặt *=a

\(\overline{57a3}⋮9\)

=>\(5+7+a+3⋮9\)

=>\(a+15⋮3\)

mà 0<=a<=9

nên a=3

=>*=a

b: \(A=123\cdot7+8+9\)

123*7 là số lẻ

9 là số lẻ

=>123*7+9 chia hết cho 2

mà 8 chia hết cho 2

nên \(A=123\cdot7+9+8⋮2\)

\(123\cdot7⋮3;9⋮3;8⋮̸3\)

=>\(A=123\cdot7+9+8⋮̸3\)

c: \(B=3\cdot5\cdot7+10^{50}\)

\(=5\cdot3\cdot7+5\cdot5^{49}\cdot2^{49}\)

\(=5\left(3\cdot7+5^{49}\cdot2^{49}\right)⋮5\)

=>B là hợp số

1) 25 + 91 + 75 + 101

= (25+75) + (91 + 101)

= 100 + 192

= 292

2) 41 x 39 - 41 x 9

= 41 x (39 - 9)

= 41 x 30

= 1230

3) 710 x 99 + 710

= 710 x 99 + 710 x 1

= 710 x (99 + 1)

= 710 x 100

= 71000

4) 17 x 85 + 15 x 17 - 120

= 17 x (85 + 15) - 120

= 17 x 100 -120

= 1700 -120

= 1580

5) (39 x 42 - 37 x 42) : 42

= 42 x (39 - 37) : 42

= 42 x 2 : 42

= 84 : 42

=2

6) 120 - 48 - 52

= 120 - (48 + 52)

= 120 - 100

= 20

7) 23 x 75 + 25 x 23 + 180

= 23 x (75 + 25) +180

= 23 x (75 + 25) +180

= 23 x 100 + 180

= 2300 +180

=2480

8) 2448 : [119 - (23 - 6)]

= 2448 : (119 - 17)

= 2448 : 102

= 24 

\(4\cdot5^2-3\cdot2^3+3^3\cdot3^2\)

\(=4\cdot25-3\cdot8+3^{2+3}\)

\(=100-24+3^5\)

\(=100-24+243\)

\(=343-24\)

\(=319\)

a) 100:{250:[450−(4.53−25.4)]}100:{250:[450−(4.53−25.4)]}

=100:{250:[450−(4.125−25.4)]}=100:{250:[450−(4.125−25.4)]}

=100:{250:[450−(500−100)]}=100:{250:[450−(500−100)]}

=100:[250:(450−400)]=100:[250:(450−400)]

=100:(250:50)=100:(250:50)

=100:5=100:5

=20=20

b) 4(18−15)−(5−3).324(18−15)−(5−3).32

=4.3−2.32=4.3−2.32

=4.3−2.9=4.3−2.9

=12−18=12−18

​=−6=−6

\(B=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+\frac{1}{18\cdot19\cdot20}\)

\(B=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+\frac{2}{18\cdot19\cdot20}\right)\)

\(B=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{18\cdot19}-\frac{1}{19\cdot20}\right)\)

\(B=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{19\cdot20}\right)\)

\(B=\frac{1}{2}\cdot\frac{189}{380}=\frac{189}{760}\)

\(C=\frac{52}{1\cdot6}+\frac{52}{6\cdot11}+\frac{52}{11\cdot16}+...+\frac{52}{31\cdot36}\)

\(C=\frac{52}{5}\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+...+\frac{6}{31\cdot36}\right)\)

\(C=\frac{52}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{31}-\frac{1}{36}\right)\)

\(C=\frac{52}{5}\cdot\left(1-\frac{1}{36}\right)\)

\(C=\frac{91}{9}\)

80 − (4 . 52 – 3 . 23)

= 80 – ( 4 . 25 – 3 . 8)

= 80 – (100 – 24 )

= 80 – 76 = 4