id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
11,095 |
(a + g) \cdot (a + g) = g^2 + a^2 + a\cdot g\cdot 2
|
11,686 |
(X + Z) E = ZE + XE
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-160 |
\frac{1}{(3*(-1) + 10)!}*10! = 10*9*8
|
-13,648 |
7 + 6\cdot 5 - 2\cdot 8 = 7 + 30 - 2\cdot 8 = 37 - 2\cdot 8 = 37 + 16\cdot (-1) = 21
|
6,915 |
\frac{1}{114} = 10/1140
|
34,318 |
\sqrt{3}*18 = \frac{1}{x^3} + x^3\Longrightarrow x^6 - 18*\sqrt{3}*x^3 + 1 = 0
|
36,632 |
(2^{1/2} - 1) \cdot (2^{1/2} - 1) = (-2^{1/2} + 1)^2
|
-3,572 |
\frac{1}{q^2} \cdot q = \frac{q}{q \cdot q} = \dfrac1q
|
52,730 |
\frac{1}{\sqrt{3}} = \frac{1}{\sqrt{3}} * 1 = \frac{1}{\sqrt{3}} *\frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}
|
23,087 |
\sqrt{x} * x^2 = x^{1/2}*x^2=x^{2 + 1/2} = x^{5/2}
|
4,647 |
0*z + 0*z^2 + z^3 + ... + z^{(-1) + k} + z^k = \frac{1}{z + \left(-1\right)}*(z^{k + 1} - z^3)
|
4,157 |
\sec(\pi/2 - x) = \csc(x)
|
3,190 |
(1 + 3 \cdot 3) \cdot (1 + 3^4) \cdot ((-1) + 3^2) = 3^{2^3} + (-1)
|
33,047 |
\mathbb{E}[U \cdot U \cdot U] = \mathbb{E}[-U]^3 = -\mathbb{E}[U^3]
|
26,309 |
z^W Az = z^W A^W z = -z^W A
|
25,399 |
(-p \cdot b + a \cdot q)^2 + (q \cdot b + p \cdot a)^2 = (a^2 + b^2) \cdot \left(q^2 + p^2\right)
|
19,985 |
\frac{1}{(1 + 0) e} = \frac{1}{e}
|
13,693 |
\frac{2 \cdot r \cdot \pi}{2 \cdot \pi} = r
|
22,155 |
2 \cdot 3^0 + 3^1 \cdot 2 + 2 \cdot 3^2 + ... + 3^{\alpha + (-1)} \cdot 2 = 3^\alpha + (-1)
|
-20,356 |
\frac{-18\cdot x + 3\cdot (-1)}{5 + 30\cdot x} = -\frac{1}{5}\cdot 3\cdot \frac{x\cdot 6 + 1}{1 + 6\cdot x}
|
-26,552 |
2\cdot z^2 - 40\cdot z + 200 = 2\cdot (z \cdot z - 20\cdot z + 100) = 2\cdot (z + 10\cdot \left(-1\right))^2
|
567 |
(Y + x)^2 = x^2 + Y \cdot Y + Y \cdot x \cdot 2
|
8,721 |
11 = 18 + 5(-1) + 2(-1)
|
26,280 |
\left(x + 1\right) \cdot \left(x + 1\right) = 1 + x^2 + x\cdot 2
|
3,038 |
\left(-x\right) * \left(-x\right) * \left(-x\right) = -x*(-x) * (-x) = -x*x * x = -x * x * x
|
1,306 |
0 < q, 0 < 96 \cdot (-1) + q \cdot 5 \Rightarrow q > \frac15 \cdot 96 = 19.2
|
14,639 |
x\cdot h = x\cdot h/x\cdot x
|
-20,825 |
\frac{(-28) \cdot k}{7 \cdot (-1) + 7 \cdot k} = \frac{7}{7} \cdot \frac{1}{(-1) + k} \cdot (k \cdot (-4))
|
26,239 |
24 = Z\cdot z \implies \frac{\mathrm{d}Z}{\mathrm{d}t}\cdot z + Z\cdot \frac{\mathrm{d}z}{\mathrm{d}t} = 24
|
-5,489 |
\frac{3}{14 + r^2 + r \cdot 9} = \frac{3}{(2 + r) (7 + r)}
|
44,802 |
1024 = 1\cdot 2^{10}
|
50,967 |
24 = 3\cdot 4\cdot 2
|
23,006 |
76923 = \frac{1}{13}\times (-1 + 10^6)
|
32,162 |
m + (-1) = 0\Longrightarrow 1 = m
|
-270 |
\tfrac{7!}{(7 + 6(-1))! \cdot 6!} = {7 \choose 6}
|
19,698 |
\sin{\dfrac{π*4}{3}1} = \sin{-\frac13π}
|
8,359 |
\binom{l}{y} = \dfrac{l!}{y! \cdot (-y + l)!}
|
37,068 |
AA^C = A^C A
|
4,221 |
\dfrac{3\pi}{4} = \pi*9/12
|
-10,748 |
-\frac{1}{40\cdot r^3}\cdot 60 = 10/10\cdot (-\frac{6}{4\cdot r^3})
|
33,671 |
\left\lceil{\dfrac{1}{3\cdot (-1) + \pi}}\right\rceil = 8
|
-7,967 |
\tfrac{1}{25} \cdot (-21 + 72 \cdot i + 28 \cdot i + 96) = \tfrac{1}{25} \cdot (75 + 100 \cdot i) = 3 + 4 \cdot i
|
34,924 |
\frac{\delta_{a_i}}{2} = \delta_{a_i}
|
20,468 |
(-y + z)\cdot (y + z) = z^2 - y^2
|
13,654 |
\tan^{-1}(1)=\frac{\pi}{4}
|
-11,959 |
\frac{1}{15}*14 = \frac{1}{4*\pi}*s*4*\pi = s
|
19,804 |
2^3 + 2^3 + 2^3 = 2^4 + 2^2 + 2 \cdot 2
|
33,160 |
F = (F \cap W) \cup (F \cap Y') = F \cap (W \cup Y')
|
6,031 |
x^3 + v \cdot v^2 = (v^2 + x^2 - x\cdot v)\cdot (x + v)
|
10,876 |
\sin{a}\cdot \cos{b} = (\sin(a + b) + \sin(-b + a))/2
|
14,218 |
\sin{x} = \cos(\pi/2 - x) = \cos{2 (\pi/4 - x/2)}
|
26,921 |
25 (-1) + 25 = 25 \left(-1\right) + 25
|
-98 |
-28 + 5*\left(-1\right) = -33
|
-30,747 |
(y^2 + 2\cdot \left(-1\right))\cdot 9 = 18\cdot (-1) + 9\cdot y^2
|
3,292 |
a^2 + b^2 = \left(a + b + (a\cdot b\cdot 2)^{1/2}\right)\cdot (-(a\cdot b\cdot 2)^{1/2} + a + b)
|
20,262 |
2 \cdot \cos^2{\dfrac{1}{2} \cdot x} + (-1) = \cos{x}
|
-1,990 |
-\pi/4 + 3/2 \times \pi = \dfrac{5}{4} \times \pi
|
11,894 |
-(z + 10 \cdot (-1)) \cdot \left(z + 4 \cdot (-1)\right) = -40 + 14 \cdot z - z^2
|
-17,282 |
0.767 = \frac{1}{100}\cdot 76.7
|
30,192 |
20683 = 10^3 + 27 27 27 = 19^3 + 24^3
|
22,156 |
\frac{3 - 1 + 2 + 4}{1\times 2 - 3\times 4} = 4/\left(-10\right) \neq 0
|
-26,658 |
(3 + y) \cdot (1 + 2 \cdot y) = 2 \cdot y \cdot y + 7 \cdot y + 3
|
27,403 |
1 - \frac{6}{20} = \frac{1}{10}*7
|
-5,781 |
\tfrac{2}{z\cdot 5 + 40\cdot (-1)} = \dfrac{1}{5\cdot (8\cdot (-1) + z)}\cdot 2
|
-19,424 |
9*\frac{1}{8}/(7*1/6) = \dfrac{6}{7}*\frac98
|
4,658 |
\int\limits_{-1}^1 (a + h)^2\,\mathrm{d}z = \int \left(a^2 + \int (h^2 + 2\times \int a\times h\,\mathrm{d}z)\,\mathrm{d}z\right)\,\mathrm{d}z = \int (a^2 + \int h \times h\,\mathrm{d}z)\,\mathrm{d}z
|
25,761 |
\frac{1/4 \cdot 3}{2 \cdot \frac13} = \frac{9}{8}
|
32,531 |
2^{m + 1} - 2^m = 2^m \cdot (2 + (-1)) = 2^m
|
-20,671 |
\dfrac{1}{m + 4\cdot (-1)}\cdot (7 + m)\cdot 10/10 = \frac{1}{10\cdot m + 40\cdot (-1)}\cdot (m\cdot 10 + 70)
|
520 |
20 + 6*(-1) + 8*(-1) = 6
|
23,437 |
((-1) + x \cdot 2) \cdot (2 \cdot x + 3 \cdot (-1)) \cdot (5 \cdot (-1) + 2 \cdot x) \cdot \cdots = (((-1) + 2 \cdot x)!)!
|
-4,641 |
\frac{13 + 2 \cdot z}{20 + z^2 + 9 \cdot z} = -\tfrac{3}{z + 5} + \frac{5}{z + 4}
|
22,451 |
162 ((-1) + k) + 126 = (2 (-1) + k)*180 \Rightarrow 18 = k
|
19,775 |
\frac{mx}{m * m}1 = \dfrac{x}{m}
|
21,333 |
(5*(-1) + x)*(x + 1) * (x + 1) = (x^2 - 4*x + 5*\left(-1\right))*(1 + x)
|
6,023 |
6/2 \times \left(2 + 1\right) = 9
|
21,511 |
\cos^3\left(π\right) = (-1)^3 = -1
|
44,032 |
{6\choose 1} = 6
|
-2,454 |
( 5 + 1 )\sqrt{10} = 6\sqrt{10}
|
-1,073 |
-8/1 \cdot \frac{8}{9} = \frac{1/9 \cdot 8}{(-1) \cdot 1/8}
|
6,682 |
0 = x^2 + 4 \times x + 5 \times (-1)\Longrightarrow 0 = (x + 5) \times ((-1) + x)
|
-21,052 |
\frac18 \cdot 4 = 2/4 \cdot 2/2
|
29,441 |
\frac{1}{3} + \frac13 = \frac{2}{3}
|
505 |
(g^2 + b^2)^3 = 8^2 = 64 rightarrow g * g + b * b = 4
|
12,267 |
\frac1n \leq 1\Longrightarrow 1 + \dfrac1n \leq 2
|
9,601 |
\frac{x^i}{g} \cdot g = (x/g \cdot g)^i
|
12,438 |
1 = -397 \cdot 42094239791738433660^2 + 838721786045180184649^2
|
16,266 |
5\cdot \tan^2{\frac{π}{10}} + 10\cdot (-1) + \cot^2{\frac{π}{10}} = 0
|
3,567 |
b' x + 1 = 2(b' + x)
|
13,785 |
\dfrac{3*8}{6} = 4
|
16,167 |
\binom{l}{k} = \frac{l!}{k!\cdot (l - k)!} = \binom{l}{l - k}
|
-19,069 |
17/40 = \frac{1}{64 \cdot \pi} \cdot X_r \cdot 64 \cdot \pi = X_r
|
-20,610 |
\frac{1}{28 - 20 r} (63 (-1) + 45 r) = \dfrac{-r\cdot 5 + 7}{7 - 5 r} (-\frac94)
|
-1,078 |
-\dfrac{10}{6} = \left(\left(-10\right) \dfrac12\right)/(6\cdot \frac12) = -\dfrac13 5
|
21,554 |
1 + \dotsm + p^{m + 1} = \frac{1}{1 - p}\cdot \left((1 - p)\cdot p^{m + 1} + 1 - p^{m + 1}\right)
|
25,205 |
\left(x + b\right)\cdot \sqrt{2} + a + a' = a' + x\cdot \sqrt{2} + a + \sqrt{2}\cdot b
|
28,030 |
\frac{\mathrm{d}}{\mathrm{d}x} \tan(x) = 1 + \tan^2(x) = \sec^2(x)
|
10,499 |
6 - \tan^2\left(\frac{\pi}{10}\right)*2 = \cot^2(\pi/10) + 4 (-1) + \tan^2(\pi/10)*3
|
30,416 |
134 = 11^2 + 3 * 3 + 2^2 = 10^2 + 5 * 5 + 3^2 = 9^2 + 7^2 + 2^2 = 7^2 + 7^2 + 6^2
|
7,434 |
x^3 = (x + (-1) + 1)^3 = (x + (-1))^3 + 3 \cdot \left(x + (-1)\right)^2 + 3 \cdot \left(x + (-1)\right) + 1
|
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