a) \(82\cdot78\)

\(=\left(80+2\right)\cdot\left(80-2\right)\)

\(=80^2-2^2\)

\(=6400-4\)

\(=6396\)

b) \(87\cdot93\)

\(=\left(90-3\right)\left(90+3\right)\)

\(=90^2-3^2\)

\(=8100-9\)

\(=8091\)

c) \(125^2-25^2\)

\(=\left(125-25\right)\left(125+25\right)\)

\(=100\cdot150\)

\(=15000\)

Bài 3:

a: Ta có: \(23\left(42-x\right)=23\)

\(\Leftrightarrow42-x=1\)

hay x=41

b: Ta có: 15(x-3)=30

nên x-3=2

hay x=5

Bài 1: 

a: 32+89+68=100+89=189

b: 64+112+236=300+112=412

c: \(1350+360+650+40=2000+400=2400\)

a 60 - 26,75 - 13,25

= 60 - ( 26,75 + 13,25 )

= 60 - 40

= 20

b ) 45,78 + 38,42 - 25,78 - 18,42

= ( 45,78 - 25,78 ) + ( 38,42 - 18,42 )

= 20 + 20

= 40

a=20

b=40

c=7290

d=26

a,60-26.75-13.25

=60-26.3.25-13.25

=60-78.25-13.25

=60-25.(78+13)

=60-2275

=-2215

a, = 996 + 4 + 40 = 1000 + 40 = 1040

b, = 198 + 2 + 35 = 200 + 35 = 235

c, = ( 4 *25 )*(2 * 5)*55=100 * 10 * 55 = 55000

d, = 97*(36+64) = 97 * 100 = 9700

e, = (125+75)+(360+40)= 200 + 400 = 600

g, =10^2=100

a) \(996+44\)

    \(=1040\)

b) \(37+198\)

     \(=230\)

\(a,996+44=1040\)                                                                 

\(d,97.36+64.97=97.\left(36+64\right)=97.100=9700\)

\(b,37+198=235\)

\(c,4.55.25.2.5=220.50.5=11000.5=55000\)

\(e,125+360+75+40=485+115=600\)

\(g,10^{12}:10^{10}=10^2=100\)

 Bài 1: Thực hiện phép tính:

\(\text{a, 1,3 + 2,5 – 4,7 + 5,6 – 4,3=}0,4\)

\(\text{b, - 5,7 + 4,2 – 8,2 + 11,7}=2\\ \)

\(\text{c, 25.(- 0,8).4.(-0,5).0,224}=8,96\)

Bài 3: Tính nhanh:

\(\text{a, -13,45 – 7,98 – 8,55}=-29,98\)

\(\text{b, 9,72 + 8,38 + 3,62}=21,72\)

\(c,\)\(\)\(\left| {45,37} \right| - \left| { - 29,73} \right| + \left( { - 12,27} \right)\)\(=45,37-29,73-12,27=3,38\)

\(\text{d, 31,71 – 7,41.15 – 2,59.15}=-118,29\)

Bài 1:

a) \(1,3+2,5-4,7+5,6-4,3\) 

\(=\left(1,3+2,5+5,6\right)+\left(-4,7-4,3\right)\) 

\(=9,4+\left(-9\right)\) 

\(=0,4\) 

b) \(-5,7+4,2-8,2+11,7\) 

\(=\left(-5,7+11,7\right)+\left(4,2-8.2\right)\) 

\(=6+\left(-4\right)\) 

\(=2\) 

c) \(25.\left(-0,8\right).4.\left(-0,5\right).0,224\) 

\(=\left(25.4\right).\left(-0,8.-0,5\right).0,224\) 

\(=100.0,4.0,224\) 

\(=40.0,224\) 

\(=8,96\)

Bài 2.

a) 101³ = (100+1)³ = 100³+3.100².1+3.100.1²+1³ 

   = 1000000+30000+300+1 = 1030301

b) 299³ = (300-1)³ = 300³-3.300².1+3.300.1²-1³

   = 27000000 - 270000 + 900 -1 = 26730899

c) 99³ = (100-1)³ = 100³-3.100².1+3.100.1²-1

   = 1000000 - 30000 + 300 -1 = 970299

\(1,\\ b,A=\left(u-v\right)^3+3uv\left(u+v\right)\\ A=u^3-3u^2v+3uv^2-v^3+3u^2v+3uv^2=u^3-v^3\\ c,6\left(c-d\right)\left(c+d\right)+2\left(c-d\right)^2-\left(c-d\right)^3\\ =6c^2-6d^2+2c^2-4cd+2d^2-c^3+3c^2d-3cd^2+d^3\\ =8c^2-c^3-4d^2-4cd+3c^2d-3cd^2+d^3\)

\(2,\\ a,101^3=\left(100+1\right)^3\\ =100^3+3\cdot10000\cdot1+3\cdot100\cdot1+1\\ =1000000+30000+300+1=1030301\\ b,299^3=\left(300-1\right)^3\\ =300^3-3\cdot90000\cdot1+3\cdot300\cdot1-1\\ =27000000-270000+900-1\\ =26730899\\ c,99^3=\left(100-1\right)^3\\ =100^3-3\cdot10000\cdot1+3\cdot100\cdot1-1\\ =1000000-30000+300-1=970299\)

Bài 1:
a.

$A=u^3-3u^2v+3uv^2-v^3+3uv^2+3u^2v$

$=u^3+6uv^2-v^3$

c.

$C=(c-d)[6(c+d)+2(c-d)-(c-d)^2]$

$=(c-d)[8c+4d-(c^2-2cd+d^2)]=(c-d)(-c^2+2cd-d^2+8c+4d)$

a: \(20-\left[30-\left(5-1\right)^2\right]\)

\(=20-\left[30-4^2\right]\)

\(=20-14=6\)

b: \(71+\dfrac{50}{5+3\left(57-6\cdot7\right)}\)

\(=71+\dfrac{50}{5+3\cdot\left(57-42\right)}\)

\(=71+\dfrac{50}{5+3\cdot15}=71+\dfrac{50}{50}=72\)

c: \(4\cdot\left\{270:\left[50-\left(2^5+45:5\right)\right]\right\}\)

\(=4\cdot\left\{270:\left[50-32-9\right]\right\}\)

\(=4\cdot\left\{\dfrac{270}{50-41}\right\}=4\cdot\dfrac{270}{9}=4\cdot30=120\)

d: \(411-\left[\dfrac{\left(107+3\right)}{5}-2^2\right]\)

\(=411-\left[\dfrac{110}{5}-4\right]\)

=410-22+4

=410-18

=392

e: \(450-5\left[3^2\left(7^5:7^3-41\right)-12\right]+18\)

\(=450-5\left[9\cdot\left(7^2-41\right)-12\right]+18\)

\(=450-5\cdot\left[9\cdot8-12\right]+18\)

=468-5*60

=468-300

=168

f:

\(102-150:\left[18-2\cdot\left(10-8\right)^2\right]+1018^0\)

\(=102-150:\left[18-2\cdot4\right]+1\)

\(=103-\dfrac{150}{18-8}=103-15=88\)

a. A = (a + b)³ - (a - b)³

A = \(\left[\left(a+b\right)-\left(a-b\right)\right]\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)

A = (a + b - a + b)\(\left[a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right]\)

A = 2b(a² + a² + a² + 2ab - 2ab + b² - b² + b²)

A = 2b(3a² + b²)

A = 6a²b + 2b³

a: \(=\dfrac{\left(\dfrac{1}{2}:\dfrac{1}{2}-\dfrac{1}{4}:\dfrac{1}{4}+\dfrac{1}{8}:\dfrac{1}{8}-\dfrac{1}{10}:\dfrac{1}{10}\right)}{1+2+3+...+2008}\)

=0

c: =8,1*5/3*1875+13,5*625

=13,5(1875+625)

=13,5*2500

=33750