id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
17,599 |
X^3 + 1 = \left(1 + X\right)\times (X^2 - X + 1)
|
-9,342 |
p \cdot 27 = 3 \cdot 3 \cdot 3 p
|
42,463 |
1=1*8-1*7=1*8-1*(23-2*8)
|
33,375 |
(3 \cdot z + 2 \cdot (-1)) \cdot \left(5 + z\right) = 10 \cdot (-1) + 3 \cdot z^2 + z \cdot 13
|
14,024 |
-\dfrac{1}{\tau} = 5*i = 25*\tau
|
-2,610 |
\sqrt{250} - \sqrt{40} = \sqrt{25 \cdot 10} - \sqrt{4 \cdot 10}
|
12,947 |
30 \cdot 7!/9! = \frac{30}{72} = \frac{5}{12}
|
17,338 |
2\cdot (a + \frac{1}{2}\cdot (z + y)) = y + a + z + a
|
-26,515 |
(3*(-1) + 5*x)^2 = 9 + 25*x^2 - 30*x
|
-7,601 |
\dfrac{-7+22i}{3-2i} = \dfrac{-7+22i}{3-2i} \cdot \dfrac{{3+2i}}{{3+2i}}
|
8,512 |
x a + b x = \left(b + a\right) x
|
34,492 |
\frac12\cdot (\left(-1\right)\cdot \pi) = -\dfrac{\pi}{2}
|
-7,116 |
1/6 = \frac39*\frac{4}{8}
|
-2,076 |
13/12 \cdot \pi = \pi/3 + \pi \cdot 3/4
|
10,817 |
\frac16(q^6 + q + q \cdot q + q^3 + q^4 + q^5) = q\cdot (q^5 + 1 + q + q \cdot q + q^3 + q^4)/6
|
5,187 |
(1 - x)\cdot \left(1 + x\right) = -x^2 + 1
|
25,968 |
z \cdot 4\% = z \cdot 0.04
|
-557 |
\tfrac{1}{12}\cdot \pi = -\pi\cdot 24 + \dfrac{289}{12}\cdot \pi
|
7,004 |
(-\pi + x) (x - e) = \pi e + x^2 - x*(\pi + e)
|
20,508 |
503\cdot 497 = (500 + 3)\cdot (500 + 3\cdot (-1)) = 500^2 - 3 \cdot 3 = 250000 + 9\cdot (-1) = 249991
|
18,763 |
z = x + i\cdot y \Rightarrow -x + z = i\cdot y
|
31,383 |
4 \cdot V \cdot r \cdot x^2 = x \cdot r \cdot 2 \cdot 2 \cdot x \cdot V
|
30,959 |
\left((-1) + y\right)^2 + 1 = 2 + y^2 - 2\cdot y
|
-22,714 |
10\cdot 4/(4\cdot 9) = 40/36
|
-5,441 |
2.36 \cdot 10 = \dfrac{10}{1000} \cdot 2.36 = 2.36/100
|
29,047 |
(2^{(n + (-1))/2} + (-1)) \cdot \left(2^{\frac12 \cdot \left(n + (-1)\right)} + 1\right) = (-1) + 2^{\left(-1\right) + n}
|
12,902 |
\cos(s) + \sin(s)\cdot 0 = \cos\left(s\right)
|
30,278 |
73 h_0 x_0 = h_0^2 + x_0 h_0*72 + x_0 * x_0 - x_0^2 + h_0^2 - x_0 h_0
|
26,057 |
\left(m + (-1)\right) \cdot 2 = 2 \cdot m + 2 \cdot (-1) \gt m
|
19,046 |
\dfrac{3}{3 + 2}*\dfrac{1}{3 + 2}3 = \frac{9}{25} = 0.36
|
32,095 |
0 \neq x \Rightarrow \frac{x}{x} = 1
|
19,143 |
(x + 1)^4 - x^4 = (\left(x + 1\right) \cdot \left(x + 1\right) + x \cdot x) ((x + 1) \cdot (x + 1) - x^2) = (2x^2 + 2x + 1) \left(2x + 1\right)
|
14,255 |
31 + 8 \cdot \sqrt{15} = \left(a + b \cdot \sqrt{15}\right)^2 = a^2 + 15 \cdot b^2 + 2 \cdot a \cdot b \cdot \sqrt{15}
|
25,578 |
x_m = C*F \Rightarrow F*C = x_m
|
192 |
\left(-y_0 + 2\right)^2 + (1 - y_0)^2 = y_0^2 \Rightarrow 0 = 5 + y_0^2 - y_0 \times 6
|
34,130 |
b*d \coloneqq d*b
|
-4,466 |
x^2 + x \cdot 3 + 10 \cdot (-1) = (x + 2 \cdot \left(-1\right)) \cdot (5 + x)
|
-11,956 |
\frac{1}{10} 7 = \frac{1}{8 \pi} s\cdot 8 \pi = s
|
6,077 |
(x^2 + \sqrt{2}) \cdot (-\sqrt{2} + x^2) = x^4 + 2 \cdot (-1)
|
30,825 |
(f + g)\cdot 0 = \sin(0) + \cos(0) = 0 + 1 = 1 + 0 = \sin(\dfrac{\pi}{2}) + \cos(\dfrac{\pi}{2}) = (f + g)\cdot \frac{\pi}{2}
|
12,305 |
1 = 1/2 + \frac14 + \dfrac18 + \ldots
|
20,602 |
e^{\dfrac{4}{3} \cdot \pi \cdot i} = (e^{2 \cdot i \cdot \pi/3})^2
|
-2,687 |
\sqrt{6} \times (4 + 5 \times (-1) + 3) = \sqrt{6} \times 2
|
-7,142 |
\frac{1}{7}*2*\frac{3}{6} = \tfrac{1}{7}
|
28,076 |
|x| \cdot 2 = \frac{d}{dx} \left(x \cdot |x|\right)
|
-502 |
\frac{\pi}{2} = -\pi \cdot 24 + 49/2 \cdot \pi
|
40,618 |
5 = 4 \cdot (-1) + 9
|
-7,447 |
1/12 = \frac{3}{8} \cdot \dfrac{1}{9} \cdot 4 \cdot 5/10
|
27,204 |
\sin(b)*\sin(g) + \cos(g)*\cos(b) = \cos(g - b)
|
-18,254 |
\frac{1}{x^2 - x*9 + 8}*(6*(-1) + x * x + 5*x) = \dfrac{(6 + x)*\left(x + (-1)\right)}{(x + (-1))*\left(x + 8*(-1)\right)}
|
1,071 |
(n + 1)! = n! + n! \cdot n
|
-6,139 |
\frac{3h}{(h + 4) (3(-1) + h)} = \frac{3h}{h \cdot h + h + 12 (-1)}
|
25,636 |
y\cdot b\cdot c = b\cdot c\cdot y
|
34,879 |
(h - c)/4 = -\frac{c}{4} + h/4
|
-20,530 |
\frac{1}{1}\cdot 9\cdot \frac{7 - 4\cdot p}{-4\cdot p + 7} = \frac{-p\cdot 36 + 63}{-p\cdot 4 + 7}
|
48,616 |
0.5124 = 1 - 0.4876
|
9,577 |
(1 + 7)^z = 2^{z\cdot 3}
|
-3,046 |
2 \cdot 3^{1 / 2} = 3^{\frac{1}{2}} \cdot \left(1 + 5 + 4 (-1)\right)
|
14,043 |
\frac{\binom{4}{2}}{\binom{5}{3}} = \frac{6}{10} = \frac{1}{5}*3
|
17,212 |
3\cdot x^2 + 2 = 3\cdot (x^2 + (-1)) = 3\cdot (x + \left(-1\right))\cdot \left(x + 1\right) = 3\cdot (x + (-1))\cdot (x + 4\cdot \left(-1\right))
|
7,355 |
\frac{x}{\sqrt{1 + x^4}} + 0 \cdot \left(-1\right) + 0 - 0 \cdot \cdots = \dfrac{x}{\sqrt{1 + x^4}}
|
-19,036 |
\frac{7}{15} = \frac{1}{9*\pi}*X_s*9*\pi = X_s
|
-6,095 |
\dfrac{3}{5*(x + 8)} = \frac{1}{40 + 5*x}*3
|
12,197 |
1 + 2^0 + 2^1/2! + \frac{2^2}{3!} = \frac{1}{3} \cdot 11
|
24,340 |
3 \cdot a \cdot a - 12 \cdot a + 64 \cdot (-1) = 3 \cdot (16 \cdot (-1) + a^2 - a \cdot 4) + 16 \cdot (-1)
|
5,995 |
4\cdot (a'^2 \pm 10\cdot b'^2 - 10\cdot b') + 10\cdot (-1) = -(b'^2\cdot 4 + 4\cdot b' + 1)\cdot 10 + 4\cdot a' \cdot a'
|
20,751 |
z^{\frac{1}{2}}\cdot Y^{1/2}\cdot Y^{\frac{1}{2}}\cdot z^{1/2} = z\cdot Y
|
-28,798 |
150 = \tfrac{2 \cdot \pi}{\pi \cdot 2 \cdot \frac{1}{150}}
|
-19,502 |
8/7*8/7 = 1/7*8/(7*1/8)
|
-1,730 |
-\pi = 5/6*\pi - \frac{11}{6}*\pi
|
6,543 |
21 \left(-1\right) + 2014 = 1993
|
18,457 |
3 z + 4 - 2 z + 5 = z + (-1)
|
-9,468 |
-5 \cdot t + 20 \cdot (-1) = -5 \cdot 2 \cdot 2 - 5 \cdot t
|
542 |
\|z + y\|^2 = |1 + i|^2\cdot \|z\|^2 = 2\cdot \|z\|^2 = \|z\|^2 + \|y\|^2
|
20,672 |
\lim_{h \to 0} \left(25\cdot (-1) + (5 + h)^2\right)/h = \lim_{h \to 0} \tfrac1h\cdot (5 + h + 5\cdot \left(-1\right))\cdot (5 + 5 + h)
|
-3,248 |
7\cdot \sqrt{6} = \left(3 + 4\right)\cdot \sqrt{6}
|
2,555 |
1/(3\times 2) = 1/2 - 1/3
|
-11,954 |
\frac{1}{4} = \tfrac{s}{4\cdot \pi}\cdot 4\cdot \pi = s
|
-2,333 |
\dfrac{1}{11} \times 10 - \frac{1}{11} \times 4 = 6/11
|
3,194 |
exp(H + x) = exp(H) exp(x)
|
5,133 |
5/9 u = x \implies x\dfrac{9}{5} = u
|
21,540 |
0.25 = \left(0.5 - 0.25\right)
|
17,849 |
x^{\frac{1}{3}} = x^{\frac{2}{6}}
|
-23,598 |
\frac{4}{35} = \frac{2}{5}\times 2/7
|
-26,972 |
\sum_{n=1}^\infty \dfrac{3}{n*4^n}(3 + 1)^n = \sum_{n=1}^\infty \frac{3*4^n}{n*4^n} = \sum_{n=1}^\infty \frac{3}{n} = 3\sum_{n=1}^\infty \dfrac1n
|
23,053 |
\frac{c + 1}{b + 1} = \dfrac{1}{1 + b}*(1 + c)
|
16,448 |
y^{3\cdot \left(2 l + 3\right)} = y^{3\cdot (2 l + 1) + 6} = y^{3\cdot (2 l + 1)} y^6
|
12 |
\csc{2\cdot s} - \cot{2\cdot s} = \tan{s}
|
-26,410 |
\tfrac{1}{a^3} a^5 = a^{5 - 3} = a^{5 + 3 \left(-1\right)} = a^2
|
10,794 |
0 = \frac{1}{2} + X_2\Longrightarrow -1/2 = X_2
|
19,390 |
0 = a * a m - a^2 + 1 - m \Rightarrow ((-1) + m) (a^2 + (-1)) = 0
|
11,548 |
t + t = (t + t)^2 = (t + t)\cdot (t + t) = t^2 + t^2 + t^2 + t^2 = t + t + t + t
|
7,937 |
c^{p + x} = c^x \cdot c^p
|
3,055 |
|x| + 3 \cdot (-1) = 3 \cdot \left(-1\right) + |-x|
|
27,063 |
(1/2 + c)^k + (g + 1/2)^k = \frac{1}{2^k}\cdot (\left(1 + c\cdot 2\right)^k + \left(1 + g\cdot 2\right)^k)
|
22,323 |
(m + (-1))\cdot (m + 3) = m^2 + 2\cdot m + 3\cdot (-1)
|
14,700 |
\frac{1}{x^2 + 3 \cdot (-1)} \cdot (1 + 3 \cdot x^2) + 3 \cdot (-1) = \dfrac{10}{x^2 + 3 \cdot \left(-1\right)}
|
18,563 |
\sin(x \cdot 4) = -\sin(x) \cdot \cos(x) \cdot 4 + \cos^3(x) \cdot \sin(x) \cdot 8
|
5,950 |
E[E[X]] = E[X]
|
14,690 |
-10 z = 1 +- \sqrt{4z^4 - 4z^2 + 1} = 1 +- \sqrt{(2z^2 + (-1))^2}
|
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