a) \(\left(-1\right)\left[5^2-\left(4^3\right)\right]=\left(-1\right)\left(25-64\right)=\left(-1\right)\left(-39\right)=39\)

b) \(71.64-32.\left(-7\right)+32.11=142.32+32.7+32.11\)

\(=32.\left(142+7+11\right)=32.\left(142+18\right)=32.160=5120\)

c) \(666-\left(-422\right)-100-88=666+422-100-88\)

\(=\left(666+422\right)-\left(100+88\right)=1088-188=900\)

d) \(23-501-343+61-257+16-499\)

\(=\left(23+61+16\right)-\left(501+499\right)-\left(343+257\right)\)

\(=100-1000-600=100-\left(1000+600\right)=100-1600=-1500\)

Bài 1:

6a+1 \(⋮\)2a-1

=> 2a-1\(⋮\)2a-1

=> (6a+1)- 3(2a-1) \(⋮\)2a-1

=> (6a+1) - ( 6a-3) \(⋮\)2a-1

=> 6a+1 -6a+3\(⋮\)2a-1

=> 4 \(⋮\)2a-1

=> 2a-1\(\in\)Ư(4)

Còn j bn làm nốt nhoaaa

1. Ta có \(6a+1⋮2a-1\)

\(\Rightarrow3\left(2a-1\right)+4⋮a-1\)

\(\Rightarrow4⋮a-1\)

\(\Rightarrow a-1\inƯ\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)

\(\Rightarrow a\in\left\{-3;-1;0;2;3;5\right\}\)  ( thỏa mãn a nguyên )

Vậy \(a\in\left\{-3;-1;0;2;3;5\right\}\)

2. a,     x - y - ( - y + a + x)

= x - y + y - a - x

= - a

b, (-90) - (b + 10) + 100

= - 90 - b - 10 + 100

= ( - 90 - 10 +100) - b

= 0 - b

= - b

@@ Học tốt

\(5.\left(-8\right).2.\left(-3\right)=\left[5.\left(-8\right)\right]\left[2.\left(-3\right)\right]=\left(-40\right)\left(-6\right)=240\)

\(\left(-3\right).4.\left(-5\right).\left(-7\right)=\left[\left(-3\right).4\right]\left[\left(-5\right)\left(-7\right)\right]=\left(-12\right).35=-420\)

\(3.\left(-5\right)^2+2.\left(-5\right)-20=3.25-10-20=75-30=45\)

\(34.\left(15-10\right)-15.\left(34-10\right)=34.15-34.10-15.34+15.10\)

\(=\left(15.34-34.15\right)-\left(34.10-15.10\right)=0-19.10=-190\)

\(\left(-12\right)\left(-2\right)-23+5.\left(-5\right)=24-23-25=-24\)

\(\left(-3\right)^2+\left\{54\div\left[\left(-2\right)^3+7|-2|\right]\right\}.2^2=9+54\div\left[\left(-8+7+2\right)\right].4\)

\(=9+54\div1.4=9+54.4=9+216=225\)

Ta có : \(\frac{3.5.7+9.15.21+12.20.28}{2.4.6+6.12.18+8.16.24}=\frac{3.5.7.\left(1+3.3.3+4.4.4\right)}{2.4.6.\left(1+3.3.3+4.4.4\right)}=\frac{3.5.7}{2.4.6}=\frac{5.7}{2.4.2}=\frac{35}{16}\)

3S=3^2-3^3+3^4-3^5+....-3^2013

3S+S=4S=3-3^2013

S=3-3^2013/4

\(\left|x\right|-10=-3\)

\(\Leftrightarrow\left|x\right|=-3+10\)

\(\Leftrightarrow\left|x\right|=7\)

\(\Leftrightarrow\orbr{\begin{cases}x=7\\x=-7\end{cases}}\)

Vậy ...

| x | - 10 = - 3

=> | x | = - 3 + 10

=> | x | = 7

\(\Rightarrow\orbr{\begin{cases}x=7\\x=-7\end{cases}}\)

Vậy \(x=\pm7\)

\(x+xy+x=4\)

\(\Leftrightarrow x\left(2+y\right)=4\)

Mà \(x,y\inℤ\Rightarrow2+y\inℤ\)

Do đó, \(x,2+y\) là các cặp ước của 4.

Ta có bảng sau :

Vậy : \(\left(x,y\right)\in\left\{\left(-1,-6\right);\left(1,2\right);\left(2,0\right);\left(-2,-4\right);\left(4,-1\right);\left(-4,-3\right)\right\}\)

\(\Leftrightarrow\)x(1+y+1)=4

\(\Leftrightarrow\)x(2y)=4

\(\Rightarrow\)x(2y)\(\in\)Ư4 =1,4,2,-1,-2,-4

lâp bảng

x=1\(\Rightarrow\)y=2

x=2\(\Rightarrow\)y=1

x=4\(\Rightarrow\)y= không có giá trị nào

x=-1\(\Rightarrow\)y=-2

x=-2\(\Rightarrow\)y=-1

x=-4\(\Rightarrow\)y= không có giá trị nào

A= 1+2+3+....+2015

Có số số hạng là: ( 2015-1):1+1= 2015

Tổng A là: 2015( 2015+1):2=2031120

Vậy...

B = 1+3+5+............+1017

Có số số hạng là: (1017-1):2+1= 509 số

Tổng B là: 509(1017+1):2=259081

Vậy...