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ddrg
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math_formulas

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29,741
4\cdot l^2 + 4\cdot (-1) = 4\cdot (l \cdot l + (-1)) = 4\cdot (l + 1)\cdot (l + (-1))
38,931
i + 1 = -i + i\times 2 + 1
10,969
\tan(20) = \tfrac{b}{x} \Rightarrow x \times \tan(20) = b
2,869
|A| = H \implies A^2 = |A|\cdot |A| = H\cdot H = H^2
2,706
\sin{\sigma}\cdot \cos{a} + \sin{a}\cdot \cos{\sigma} = \sin(a + \sigma)
16,117
\dfrac{2\times \tfrac13}{1/3}\times 40 = 2\times 40 = 80
31,982
1010\cdot x - 404\cdot x = 606\cdot x
20,802
15/34 = \frac{6 + 9}{14 + 20}
14,635
\left( {e_1}_1, {e_2}_1\right) + ( {e_1}_2, {e_2}_2) = ( {e_1}_1 + {e_1}_2, {e_2}_1 + {e_2}_2) = ( {e_1}_2, {e_2}_2) + ( {e_1}_1, {e_2}_1)
-22,776
\frac{27}{30} = 3\cdot 9/\left(3\cdot 10\right)
24,743
l_1\cdot (1 + l_2) = l_2\cdot l_1 + l_1
30,988
\frac{1}{5 + (-1)} \cdot (100 \cdot (-1) + 5^{25} + (-1)) = (101 \cdot \left(-1\right) + 5^{25})/4
-3,987
\dfrac{6}{a^2} = \frac{6}{a^2}
-20,690
6/1*\frac{s + 10*(-1)}{s + 10*(-1)} = \frac{60*(-1) + s*6}{s + 10*(-1)}
-24,843
745 = 252\cdot \left(-1\right) + 997
39,700
|c_1| + |c_2| = c_1 - c_2 = c_1 - c_2
-21,609
\sin(-5/6*\pi) = -0.5
-20,434
\left(5\cdot y + 6\right)/\left(-3\right)\cdot \frac99 = \frac{1}{-27}\cdot \left(45\cdot y + 54\right)
-4,079
r\cdot 2/3 = r\cdot 2/3
-19,016
\dfrac{1}{12}\cdot 11 = \tfrac{C_s}{36\cdot \pi}\cdot 36\cdot \pi = C_s
-20,638
\frac{1}{-z \cdot 21 + 14} \cdot \left(z \cdot 56 + 49 \cdot \left(-1\right)\right) = \frac{7 \cdot (-1) + 8 \cdot z}{2 - 3 \cdot z} \cdot \frac{7}{7}
40,138
6 = 2\cdot 3 = (1 + \sqrt{-5})\cdot \left(1 - \sqrt{-5}\right)
-22,759
\frac{49}{35} = \dfrac{7\cdot 7}{7\cdot 5}
-9,454
35\cdot (-1) - 15\cdot l = -3\cdot 5\cdot l - 5\cdot 7
3,755
\frac{1}{2} \cdot 45 \cdot \left(2 \cdot 79 + 44 \cdot (-4)\right) = -405
27,510
L = (L + 2)^{1 / 2} \Rightarrow L = 2
-9,818
9/25*\dfrac{9}{10} = 9*9/(25*10) = 81/250
27,638
\dfrac{1}{m!}\cdot m \cdot m = \tfrac{m}{\left(m + (-1)\right)!} < \frac{m}{(m + (-1))\cdot (m + 2\cdot (-1))}
17,587
h^{i + 1}*x = h^{1 + i}*x
37,809
2^n \cdot 2 = 2^{n + 1}
15,141
m^4\cdot 16 = -(-1)^4 + 1 + (2m)^4
33,045
|( f, d)| = |( d, f)| \leq \|f\|_2 \cdot \|d\|_2
27,491
B/C + Z/C = (B + Z)/C
32,025
4 \times x = -3 \times D^2 + D^3 \Rightarrow D^3 - D^2 \times 3 + D \times 4 - 5 \times x = -x + 4 \times D
16,243
x + x^2 + \cdots \cdot x^n = \frac{-x^n + 1}{-x + 1} \cdot x
25,426
(1 + m)^4 = m^4 + 4 \cdot m^3 + 6 \cdot m^2 + m \cdot 4 + 1
-29,567
(2 + z^5 + z*6)/z = 2/z + z^5/z + \tfrac{z*6}{z} 1
21,582
A^3 + B \cdot B^2 = (B^2 + A^2 - A\cdot B)\cdot (B + A)
36,656
1 + 3\cdot 910 = 2731
40,038
\left(-1\right)*0.01 + 1 = 0.99
12,560
b^3 + 3*b^2 + 5*b + 5 = 2 + (b + 1)^3 + (1 + b)*2
34,977
\dfrac{1}{5}*5 = 4/4
40,542
2^n/2 = 2^{\left(-1\right) + n}
6,467
1 + 2 \cdot \left((-1) + k\right) = (-1) + 2 \cdot k
24,330
g t = g t
-30,114
d/dz (2 z^2) = 2 d/dz z^2 = 2*2 z^1 = 4 z
18,653
\left(h\cdot f\right)^2 = h^2\cdot f^2
21,876
50 + 1 - 2 (-7) + 1^2 - 2*2 (-1) + 2 (-7) + 2^2 + 2 (-1) = 58
3,850
x \cdot x \cdot x + (-1) = (1 + x^2 + x)\cdot (x + (-1))
75
1/6 = 1/11 + \frac{1}{22} + \tfrac{1}{33}
31,407
\frac{n}{n} = \frac1n\cdot n
-9,151
q*2*2*5 = 20 q
20,910
237 = 3 \times (-1) + 3 \times 2^6 + 2^4 \times 3
-22,051
\frac12 = \dfrac{8}{16}
-5,128
7.6\cdot 10^0 = 10^{1 - 1}\cdot 7.6
18,813
z - \sin(z) = z - z - \dfrac{z^3}{6} + ... = \frac{1}{6}*z^3 + ...
8,127
a \cdot 8 - 18 \cdot a \cdot a = 0 \Rightarrow a = \frac{8}{18} = 4/9
30,809
\frac{12}{16}*\frac{11}{15} = 132/240 = 11/20
162
\dfrac{1}{17} = \frac{1}{51} \cdot 3
2,840
2! = \dfrac{1}{3} \cdot 3! = 6/3 = 2
-3,790
\frac{1}{x}x^4*20/12 = 20 x^4/(12 x)
28,804
s^D \cdot s^A = s^{D + A}
-1,496
\dfrac{18}{45} = \tfrac{18 \cdot \tfrac{1}{9}}{45 \cdot \frac{1}{9}} = 2/5
16,825
x^4 - x^2 + 2 \cdot (-1) = x^4 + 2 \cdot x^2 + 1 = (x^2 + 1)^2
-1,407
-\frac91*9/4 = \frac14*9/((-1)*\dfrac19)
-3,343
-2^{1/2} + 32^{1/2} + 18^{1/2} = (16 \cdot 2)^{1/2} + (9 \cdot 2)^{1/2} - 2^{1/2}
18,813
y - \sin{y} = y - y - \dfrac{1}{6}\cdot y^3 + ... = \dfrac{1}{6}\cdot y \cdot y \cdot y + ...
12,546
\cos^2\left(x\right) = \frac12 \cdot (1 + \cos(x \cdot 2))
20,598
Y \cdot Z = Z^{\dfrac12} \cdot Y \cdot Z^{1/2}
-11,803
(\frac18)^2 = 1/64
22,384
8.75 = \frac19\cdot 3.15\cdot 25
29,629
-\left\lfloor{1 + \beta}\right\rfloor + \left\lfloor{1 + x}\right\rfloor = \left\lfloor{x}\right\rfloor - \left\lfloor{\beta}\right\rfloor
18,947
0 = h \cdot b rightarrow 0 = h\text{ or }b = 0
32,389
1729 = 1^3 + 12 12^2
14,835
f^{\frac13}/f = f^{\dfrac{1}{3} + (-1)} = f^{-2/3} = \frac{1}{f^{2/3}} = \dfrac{1}{f^{\frac{2}{3}}}
18,020
e^{y + i*2\pi} = e^y e^{i*2\pi} = e^y
-9,294
-48*q + 56*(-1) = -2*2*2*2*3*q - 2*2*2*7
-26,202
14/2 + 3*(-1) + 6/3 = 7 + 3*\left(-1\right) + 2 = 6
29,249
2^x - 2^{2 (-1) + x} (x + (-1)) + 2^{x + 4 (-1)} \left(2 (-1) + x\right) (x + 3 \left(-1\right))/2! - \cdots = x + 1
36,099
\sqrt{(-3)^2 + 7^2} = \sqrt{58}
1,220
\sin{\tfrac{1}{6}*\pi} = \cos{\frac{\pi}{3}} = 1/2
35,311
\tfrac{1}{ZY} = 1/(YZ) \neq \frac{1}{ZY}
28,373
158 = 2 \cdot 4^3 + 4^2 + 4^1 \cdot 3 + 2 \cdot 4^0
-6,706
\frac{1}{100} + \frac{80}{100} = \tfrac{8}{10} + 1/100
-20,395
9/9 \frac{1 + 5 k}{k + 9 \left(-1\right)} = \frac{k \cdot 45 + 9}{9 k + 81 \left(-1\right)}
9,778
(3000 + 2*x)/40 = \dfrac{3000}{40} + 2*x/40 = 75 + x/20
22,397
2/3 \cdot (1/3 \cdot 3 + \tfrac{2}{3} \cdot 2) + \frac13 = 17/9
27,138
\frac{1}{24} + \frac{1}{8} + \tfrac{1}{30} = 1/5
15,859
x = \cot{-\theta} \implies -\theta = \operatorname{arccot}(x)
14,881
\frac{1}{26}\cdot 105 = \dfrac{1}{26}\cdot 35 + \frac{35}{13}
-26,514
\left(9 \cdot (-1) + 8 \cdot x\right)^2 = (8 \cdot x) \cdot (8 \cdot x) - 2 \cdot 8 \cdot x \cdot 9 + 9^2
2,751
-\frac{1}{2^{(-1) + m}} + 2 = \frac{2^m + (-1)}{2^{m + (-1)}}
18,709
4! - 3! \cdot {4 \choose 1} + 2! \cdot {4 \choose 2} - {4 \choose 3} \cdot 1! + {4 \choose 4} \cdot 0! = 9
23,233
1 + 4 (-1) = 7 + 10 \left(-1\right) = 997 + 1000 (-1)
23,544
\cos{\xi}*\sin{\xi}*2 = \sin{\xi*2}
412
\sin{y} = \sin(-y + 2\cdot y)
11,953
1 = 35/70 + \frac{1}{296}148
-708
\left(e^{\pi \cdot i \cdot 11/12}\right)^{17} = e^{11 \cdot \pi \cdot i/12 \cdot 17}
2,091
z + \alpha/2 + \dfrac{\alpha}{2} = \alpha + z
28,862
31*0.417 = \frac{31*417}{1000}