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ddrg
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math_formulas

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int64
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12,952
\left(2 + x^2\right)*(x^4 + 4)*(2*(-1) + x * x) = x^8 + 16*(-1)
22,168
\frac{n!}{(-k + n)!} = {n \choose k}*k!
30,385
-a * a*r^2*4 + a^2*r^2 = -a^2*r * r*3
22,657
4 \cdot 4^2 = 8^2
36,958
2^{x + 1} = 2.2^x \gt x^2 + x^2
24,698
(w^{1/2})^2 = w
-15,585
\frac{1}{z^{25} \cdot \frac{1}{k^{15}} \cdot z \cdot z \cdot z} = \frac{\frac{1}{z^3}}{\dfrac{1}{k^{15}}} \cdot \frac{1}{z^{25}} = \frac{1}{z^{28}} \cdot k^{15} = \frac{k^{15}}{z^{28}}
26,129
1 = \frac{1}{y}\cdot (a - x) \Rightarrow a = x + y
3,487
x\times \left(-\frac{x}{x} + 1\right) = 0 \Rightarrow 1 = \dfrac{x}{x}
33,390
0 = |A - \mu|\Longrightarrow \mu = A
-26,668
63 = (-3)\cdot (-21)
-5,199
15.8 \cdot 10^{-2 + 4} = 10 \cdot 10 \cdot 15.8
7,658
\dfrac{1}{y + 1} = -(-\frac{1}{1 + y} + 1) + 1
-17,911
15*\left(-1\right) + 52 = 37
17,485
z^3 + 3 \cdot g \cdot z^2 + 3 \cdot z \cdot g^2 + g^3 = (z + g)^3
22,337
\sin(x\cdot 2)/2 = \sin(x) \cos(x)
-22,219
\left(5 + a\right) \cdot (a + 6 \cdot \left(-1\right)) = a^2 - a + 30 \cdot \left(-1\right)
15,654
{x \choose p} = \frac{x!}{p! \left(x - p\right)!}
17,484
(n + (-1))^3 + 3 \cdot (n + (-1)) \cdot (n + (-1)) + ((-1) + n) \cdot 3 + 1 = n^3
-10,521
-7/5 = -\dfrac75
33,921
125*x^3 + 216 = 6 * 6^2 + (5*x) * (5*x) * (5*x)
17,145
-B + B^2 = B*\left((-1) + B\right)
16,225
4 (\frac43)^{(-1) + x} = \dfrac{1}{3^{(-1) + x}} 4^x
-15,091
\tfrac{r^{10}}{\tfrac{1}{r^{20}} \dfrac{1}{z^8}} = \dfrac{r^{10}}{\frac{1}{z^8}}\frac{1}{\tfrac{1}{r^{20}}} = r^{10 - -20} z^8 = r^{30} z^8
16,185
\dfrac{5}{-3} = -\frac{5}{3}
-14,423
5 \cdot \left(6 + 10\right) = 5 \cdot 16 = 80
34,571
AC = AC
-1,087
\tfrac{1}{\dfrac76 \cdot 9} = 6 \cdot \dfrac17/9
12,295
d/3 + d/3 + d/3 = d
-18,811
x*2 = \frac{x*4}{2}
13,953
z \cdot z - y^2 = (-y + z) (z + y)
-22,301
(x + 3) \cdot (10 \cdot (-1) + x) = 30 \cdot (-1) + x^2 - 7 \cdot x
9,699
49/4 = \frac{1}{m + n}((m + n) m + n * n) = m + \frac{1}{m + n}n^2
8,899
t^2 + t^2 + t^2 + t \cdot t - t^3 - t^3 - t^3 - t^3 + t^4 = t^4 + t \cdot t\cdot 4 - t^3\cdot 4
9,990
\cos(g - b) = \sin(b)\cdot \sin(g) + \cos(g)\cdot \cos(b)
-2,450
\sqrt{25 \cdot 10} + \sqrt{10} = \sqrt{250} + \sqrt{10}
34,595
D^x \cdot C = D^x \cdot C
23,641
r_{\theta} p t + p' r_{\theta} = r_{\theta} (pt + p')
28,727
2*\left(2(-1) + 2^{n + 1}\right) = 2^{n + 2} + 4(-1)
-23,231
\dfrac{3}{4} = -\frac14 + 1
-6,555
2/2 \cdot \dfrac{3}{\left(2 \cdot (-1) + x\right) \cdot (8 + x)} = \frac{6}{2 \cdot (x + 8) \cdot \left(x + 2 \cdot (-1)\right)}
-19,346
\tfrac{9 \cdot \dfrac{1}{5}}{\frac{1}{2} \cdot 9} = \frac{9}{5} \cdot 2/9
-12,573
43 = 47 \times (-1) + 90
10,895
B_u \cdot 2 + B_s - B_u = B_u + B_s
-523
e^{16 \cdot 2 \cdot \pi \cdot i/3} = (e^{\frac{2}{3} \cdot i \cdot \pi})^{16}
3,813
E - E - Z = E \cap E \cap Z^\complement^\complement = E \cap (E^\complement \cup Z^\complement^\complement)
14,337
16 - 32 \cdot \sin{\phi} + 16 \cdot (\sin^2{\phi} + \cos^2{\phi}) = 32 \cdot (-\sin{\phi} + 1)
21,467
(k + x)^2 = x^2 + kx*2 + k^2
24,775
7 + x^2 - x*2 = (x + \left(-1\right)) * (x + \left(-1\right)) + 6
24,026
\frac{1}{n + \left(n^2 + 1\right)^{1/2}} = (1 + n^2)^{1/2} - n
34,228
121 = \left((-1) + 3^5\right)/2
-6,386
\tfrac{i}{(6 + i) (9 + i)}\cdot 9/9 = \frac{9i}{9(i + 6) (i + 9)}
-22,199
q^2 - q\cdot 3 + 54\cdot (-1) = \left(q + 9\cdot (-1)\right)\cdot (q + 6)
2,944
\tfrac{1}{1*2} + \tfrac{1}{1*2} = 1
28,904
(i + j + 2(-1)) (i + j + (-1))/2 = \sum_{k=1}^{i + j + 2\left(-1\right)} k = \sum_{k=2}^{i + j + \left(-1\right)} (k + (-1))
-3,574
\frac{4}{5 \cdot t} = \dfrac{4}{t} \cdot \frac{1}{5}
-545
-\pi*10 + \pi*11 = \pi
17,318
\frac12*x + \frac{1}{2}*x = x
15,638
X^2 + (-1) = \left(X + 1\right)*((-1) + X)
-11,551
-3i - 3 = -3 + 0(-1) - 3i
37,062
j = A \cup H \backslash A \cap H = A j \cup H j
-6,699
9/100 + 0/10 = \frac{9}{100} + \frac{0}{100}
25,611
(x + (-1))^3 + x^2 \cdot 2 + (\left(-1\right) + x)^2 - x = x^3
-22,991
\frac{3\times 11}{4\times 11} = \frac{1}{44}\times 33
35,915
3125 = 625 \cdot 5
18,588
h_l/\left(h_0\right) = r^l \Rightarrow h_l = r^l*h_0
19,480
1 + g > 0\Longrightarrow |g + 1| = g + 1 = g + 2
10,785
-113\cdot \left(n + 34\right) + \left(62 + n\right)^2 = n^2 + 11\cdot n + 2
13,334
\sqrt{5} = 5^{1/2} = (5 \cdot 5 \cdot 5)^{1/6}
32,782
F \cup Z \backslash F = F \cup (Z \cap F^\complement) = (F \cup Z) \cap \left(F \cup F^\complement\right) = F \cup Z
-11,541
21\cdot i - 15 + 6 = -9 + i\cdot 21
-1,975
\frac{7}{4} \cdot π + \frac{1}{3} \cdot π = \frac{1}{12} \cdot 25 \cdot π
5,735
1 - 2 \cdot i = -i^2 + (i + (-1))^2
29,302
\dfrac{4}{5 + 4} = \frac19 \cdot 4
13,029
55^{\frac{1}{2}}\cdot 4 + 31 = 4\cdot 5^{\frac{1}{2}}\cdot 11^{1 / 2} + 31
23,214
1300\cdot 3/(1\cdot 27405) = 3900/27405
4,268
x^2\cdot 25 - x^2\cdot 16 = 9x^2
10,762
\frac{1}{3 + 2l}(1 + l) = \frac{1}{2}(-\dfrac{1}{2l + 3} + 1)
29,199
\tfrac{2}{(2^{\frac{1}{3}})^2} = 2^{1/3}
13,635
(z - y)^2 = z^2 - 2 \cdot y \cdot z + y^2
2,866
\sin{t} = 0 = \sin{l*\pi} \implies \pi*l = t
-4,673
\dfrac{1}{x^2 + (-1)} \cdot (2 \cdot (-1) - x \cdot 4) = -\frac{1}{x + 1} - \frac{3}{(-1) + x}
28,060
11 = \frac{1}{3} + 4/3 \cdot 8
-5,706
\dfrac{4(k + 1)}{4(k + 9)(k + 1)} - \dfrac{8(k + 9)}{4(k + 9)(k + 1)} + \dfrac{4}{4(k + 9)(k + 1)} = \dfrac{ 4(k + 1) - 8(k + 9) + 4}{4(k + 9)(k + 1)}
9,082
2^x + l = 2 \cdot 2^{x + (-1)} + 2 \cdot \frac{l}{2} = 2 \cdot \left(2^{x + (-1)} + l/2\right)
9,013
3818\times (-9957^4 + 13083^4) = 92852^4 - 3428^4
-20,067
7s*1/(7s)/8 = 7s/\left(s*56\right)
-11,086
\left(y + 7 \cdot (-1)\right)^2 + b = \left(y + 7 \cdot (-1)\right) \cdot \left(y + 7 \cdot \left(-1\right)\right) + b = y^2 - 14 \cdot y + 49 + b
-10,278
\frac{35 + 20 \cdot x}{30 + x \cdot 15} = \frac{x \cdot 4 + 7}{6 + x \cdot 3} \cdot 5/5
41,753
1 + 2 \cdot 2 + 5 = 10
11,919
\left(\left(\frac{x}{2} = 2 \cdot x + 2 \cdot (-1) \Rightarrow x = 4 \cdot (-1) + 4 \cdot x\right) \Rightarrow 3 \cdot x = 4\right) \Rightarrow x = \dfrac{1}{3} \cdot 4
22,076
{n + n \choose n} = {2\cdot n \choose n}
14,556
\int \omega*(Uh_1 + h_2 U \alpha)\,\mathrm{d}y = \int \omega U*(\alpha h_2 + h_1)\,\mathrm{d}y
-7,023
1/8 = \frac{3}{9}\cdot \frac38
-21,720
-9/10 = -9/10
4,638
\frac{1}{\sqrt{1 + y^2}}\cdot y = \sin\left(\tan^{-1}(y)\right)
39,705
e\cdot k = e + (-1)^e\cdot k = k = k + (-1)^k\cdot e = k\cdot e
40,990
\dfrac{1}{1 + z} = 1 - \frac{z}{1 + z} \approx 1 - z
23,288
1 + \tfrac{1}{1 + \frac{1}{1 + 1^{-1}}} = 5/3
1,247
z = y + (-1) \Rightarrow z + 1 = y