a) \(45^2+33^2-22^2+90.33\)

\(=\)\(\left(45^2+33^2+2.45.33\right)-22^2\)

\(=\left(45+33\right)^2-22^2\)

\(=\left(45+33+22\right)\left(45+33-22\right)\)

\(=100.56\)

\(=5600\)

a: =-45*24+120

=-1080+120

=-960

b: =134(-1+51-48)

=134*2

=268

c: =-41*59-41*2+59*41-59*2

=-2(41+59)

=-200

a) 4 x 76 + 76 x 7
= (4 + 7) x 76
= 11 x 76
= 836
b) 4 x 54 + 54 x 2 + 5 x 54
= (4 + 4 + 5) x 54
= 13 x 54
= 702
c) 37 + 3 x 37 + 5 x 37 + 2 x 37
= 37 x (3 + 5 + 2)
= 37 x 10
= 370

a) 4 x 76 + 76 x 7
= (4 + 7) x 76
= 11 x 76
= 836
b) 4 x 54 + 54 x 2 + 5 x 54
= (4 + 4 + 5) x 54
= 13 x 54
= 702
c) 37 + 3 x 37 + 5 x 37 + 2 x 37
= 37 x (3 + 5 + 2)
= 37 x 10
= 370

a) 4 x 76 + 76 x 7

= (4 + 7) x 76

= 11 x 76

= 836.

b) 4 x 54 + 54 x 2 + 5 x 54

= (4 + 2 + 5) x 54

= 11 x 54

= 594.

c) 37 + 3 x 37 + 5 x 37 + 2 x 37

= 37 x (3 + 5 + 2 + 1)

= 37 x 11

= 407.

 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)  8,8 : 2,5 + 7,6 : 2,5 - 6,4 : 2,5

= (8,8 + 7,6 - 6,4) : 2,5

= 10 : 2,5

= 4

\(a.\)

\(8.8:2.5+7.6:2.5-6.4:2.5\)

\(=\left(8.8+7.6-6.4\right):2.5\)

\(=10:2.5\)

\(=4\)

\(b.\)

\(0.25\times1200+125\times1.5\times2-250\times2.6\)

\(=250\times1.2+250\times1.5-250\times2.6\)

\(=250\times\left(1.2+1.5-2.6\right)\)

\(=250\times0.1=25\)

\(c.\)

\(\left(32\times11-3200\times0.1-32\right):\left(81.6\times27.3-17.3\times81.6\right)\)

\(=\left[32\times\left(11-10-1\right)\right]:\left[81.6\times\left(27.3-17.3\right)\right]\)

\(=0\)

a) Ta có: \(A=\dfrac{37^3+12^3}{49}-37\cdot12\)

\(=\dfrac{\left(37+12\right)\left(37^2-37\cdot12+12^2\right)}{49}-37\cdot12\)

\(=37^2-2\cdot37\cdot12+12^2\)

\(=\left(37-12\right)^2\)

\(=25^2=625\)

Bài 4: 

a: =1267-196-267-304

=1000-500=500

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