\(a,23\cdot125+78\cdot125-125\\ =125\cdot\left(23+78-1\right)\\ =125\cdot100\\ =12500\\ b,37\cdot46+18\cdot54-17\cdot46+54\cdot2\\ =46\cdot\left(37-17\right)+54\cdot\left(18+2\right)\\ =46\cdot20+54\cdot20\\ =20\cdot\left(46+54\right)\\ =20\cdot100\\ =2000\\ b,3\cdot2^2-2^3:2+2^2\\ =3\cdot4-4+4\\ =12\\ d,7^3\cdot9+3^2\cdot7^4\\ =7^3\cdot9+7^4\cdot9\\ =7^3\cdot9\cdot\left(1+7\right)\\ =343\cdot9\cdot8\\ =24696\)

a) \(23\cdot125+78\cdot125-125\)

\(=125\cdot\left(23+78-1\right)\)

\(=125\cdot100\)

\(=12500\)

b) \(37\cdot46+18\cdot54-17\cdot46+54\cdot2\)

\(=54\cdot\left(18+2\right)+46\cdot\left(37-17\right)\)

\(=54\cdot20+46\cdot20\)

\(=54\cdot\left(20+46\right)\)

\(=20\cdot100\)

\(=2000\)

c) \(3\cdot2^2-2^3:2+2^2\)

\(=3\cdot2^2-2^2+2^2\)

\(=3\cdot2^2\)

\(=3\cdot4\)

\(=12\)

d) \(7^3\cdot9+3^2\cdot7^4\)

\(=7^3\cdot3^2+3^2\cdot7^4\)

\(=7^3\cdot3^2\cdot\left(1+7\right)\)

\(=24696\)

a: =-26+56=30

e: =-125+48+125-53=-5

a) (-124) + 24 = -100
b) 37. 78 + 37. 22
=  37 . ( 78 + 22 )
=  37 . 100
= 3700

\(a) (-124) + 24 = -100 b) 37. 78 + 37. 22 = 37 . ( 78 + 22 ) = 37 . 100 = 3700\)

a) (- 124) + 24                                          b) 37 . 78 + 37 . 22

= - ( 124 - 24)                                              =37 . ( 78 + 22)

= - 100                                                        =37 . 100 

                                                                    3700

a) 675+125+723-23

=(675+125)+(723-23)

=800+700

=1500

b) 325.40+325.60-25.100

=325.(40+60)-25.100

=325.100-25.100

=100.(325-25)

=100.300

=30000

c) 80+[37-(32+23)]

=80+(37-55)

=80-18

=62

d) 22.85+15.22-20200

=22.(85+15)-20200

=22.100-20200

=2200-20200

=-18000

\(=\left(1^2+2^2+...+100^2\right)\cdot0=0\)

a)  − 105 + − 25 + ( − 105 ) + 50  

= 105 + 25 + ( - 105) + 50

= [105 + ( -105)] + ( 25 + 50 )

= 0 + 75 = 75

b)  465 + − 38 + − 465 − 12 − − 42

= 465 + ( - 38) + ( -465) – 12 – 42

= [ 465 + (- 465) ] – ( 12 + 42 )

= 0 – 54 = 0 + ( -54 ) = -54

c)  65. − 19 + − 19 .24 + − 19 .11

= ( - 19) . ( 65 + 24 + 11 )

= ( -19) . 100 = -1900

d)  − 3 2 + 2 3 − − 5 2 + 4 3

= 9 + 8 – 25 + 64 = 56

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