id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
3,964 |
-(q + 1)\cdot 4 + q^2 = (2\cdot (-1) + q)^2 + 8\cdot (-1)
|
17,933 |
\frac{1}{2}*50 = 25
|
19,217 |
4/(2\times i) = 2/i = -2\times i
|
17,712 |
l * l - l - l + (-1) = l^2 - 2*l + 1 = (l + (-1))^2
|
28,674 |
\left(b\cdot b\cdot a = a \cdot a^2\Longrightarrow (b\cdot a\cdot b)^n = b\cdot a^n\cdot b = a^{3\cdot n}\right)\Longrightarrow a^n\cdot b = a^{n\cdot 3}\cdot b
|
-3,098 |
(5 + (-1) + 2*(-1))*5^{1/2} = 2*5^{1/2}
|
-11,161 |
(y + 7*(-1))^2 + g = (y + 7*\left(-1\right))*(y + 7*(-1)) + g = y^2 - 14*y + 49 + g
|
-16,531 |
5\cdot 9^{1 / 2}\cdot 7^{\frac{1}{2}} = 5\cdot 3\cdot 7^{1 / 2} = 15\cdot 7^{1 / 2}
|
47,627 |
\frac{3}{2}>1\implies
|
-4,578 |
\frac{-3 \cdot x + 1}{x^2 + 6 \cdot x + 5} = \dfrac{1}{1 + x} - \frac{1}{x + 5} \cdot 4
|
8,681 |
(i - c)\cdot (-i - c) = -i^2 + c^2 = 1 + c \cdot c
|
-548 |
2/3 \pi = \frac13 56 \pi - 18 \pi
|
24,055 |
\tan^{-1}(-1/4) = -\tan^{-1}\left(\dfrac14\right)
|
35,451 |
x^4 + (-1) = (x + (-1)) \cdot (x^{4 + (-1)} + x^{4 + 2 \cdot \left(-1\right)} + x^{4 + 3 \cdot (-1)} + x^{4 + 4 \cdot \left(-1\right)}) = (x + (-1)) \cdot (x^3 + x^2 + x + 1)
|
1,192 |
\cos(x)*\cos(\beta) + \sin(\beta)*\sin(x) = \cos\left(x - \beta\right)
|
32,776 |
3\cdot (3 + 1)/2 = 6
|
12,171 |
4^l + l^4 = (2^l)^2 + l \cdot l \cdot l \cdot l = (2^l + l^2)^2 - 2 \cdot 2^l \cdot l \cdot l
|
9,039 |
55*(55 \lambda^2 - \lambda*235 + 251) = (119 \left(-1\right) + \lambda*55)^2 + (55 \lambda + 119 \left(-1\right))*3 + 1
|
-26,579 |
-8^2 + z^2 = z^2 + 64 \cdot (-1)
|
17,237 |
\dfrac{k}{j} = \frac{j}{i} = \dfrac{k - j}{j - i}
|
-10,606 |
\frac33\cdot (-\dfrac{4}{t + 3\cdot (-1)}) = -\frac{12}{3\cdot t + 9\cdot (-1)}
|
18,937 |
1/2 = \dfrac{1}{4*\left(1 - 1/2\right)}
|
-20,488 |
(4 \cdot (-1) + 4 \cdot p)/(-40) = \dfrac{1}{4} \cdot 4 \cdot \dfrac{1}{-10} \cdot \left((-1) + p\right)
|
-622 |
e^{13 \frac{1}{12} i \pi \cdot 5} = (e^{5 i \pi/12})^{13}
|
993 |
y \cdot z \cdot x = 1 \implies x = 1,y = 1,z = 1
|
20,741 |
\mathbb{E}\left((X - \mathbb{E}\left(X\right))^2\right) + \mathbb{E}\left(X\right) \times \mathbb{E}\left(X\right) = \mathbb{E}\left(X \times X\right)
|
594 |
det\left(C \times P + A\right) = det\left(A + C \times P\right)
|
18,653 |
(a*d)^2 = d^2*a^2
|
-18,358 |
\frac{-6 \cdot t + t^2}{t^2 - 5 \cdot t + 6 \cdot (-1)} = \frac{t}{(1 + t) \cdot (t + 6 \cdot (-1))} \cdot (6 \cdot (-1) + t)
|
25,128 |
\phi_x \phi_x - 2 p \phi_x + x = 0 = (\phi_x - p)^2
|
15,716 |
(4 + 1)\cdot 210 = 1050
|
18,641 |
\left(-1\right) (-1) = (-1)^2 = 1
|
525 |
\left(\left(0 = \|x\|_0 rightarrow 0 = \|\mathbb{P}(x)\|_2\right) rightarrow 0 = \mathbb{P}(x)\right) rightarrow x = 0
|
-29,025 |
x^3 \cdot x^4 = x^7
|
23,193 |
2\cdot \cos^2{x} + (-1) = \cos^2{x} - \sin^2{x}
|
19,925 |
-\int_c^d f\,dx = \int\limits_d^c f\,dx
|
27,596 |
1 - \frac{1}{l^2} = \frac{\dfrac{1}{l}}{l\dfrac{1}{l + 1}}((-1) + l)
|
-10,338 |
5/5\times \dfrac{3\times c + (-1)}{2 + c\times 2} = \frac{5\times \left(-1\right) + c\times 15}{10 + c\times 10}
|
-26,613 |
49*x * x - 126*x*n + n^2*81 = (-n*9 + x*7)^2
|
37,793 |
431-38=393
|
31,259 |
\left(I = A \cdot B \Rightarrow A \cdot B \cdot B = B\right) \Rightarrow A \cdot B = I
|
-18,785 |
-\dfrac{6}{3} = -2
|
-8,354 |
(-9) = -9
|
8,352 |
7\cdot 3^2 = 8^2 + (-1)
|
9,171 |
0 = \left|{-x + H^2}\right| \Rightarrow \left|{-x + H}\right| = 0
|
4,168 |
\tfrac{a^7}{10*x^2} = \frac{(a*x)^7}{10*x^9}
|
16,745 |
y^{\frac{3}{2}} = y^1\cdot y^{\dfrac12} = y\cdot \sqrt{y}
|
26,346 |
1225 = 5 \cdot 5 \cdot 7^2
|
15,583 |
\frac{6\cdot 1/10}{\tfrac{3}{8} + \dfrac{6}{10}} = 8/13
|
12,524 |
3240 = {10 \choose 7}\cdot 3\cdot 3\cdot 3
|
49,482 |
2*z + 1 = z + 8 + 6*\sqrt{z + 8} + 9 = z + 17 + 6*\sqrt{z + 8}
|
11,479 |
\frac{1}{52}\cdot 2\cdot \frac{2}{52} = \dfrac{1}{676}
|
8,129 |
360 = (2 + 1 + 1 + 1 + 1)!/\left(1!*1!*1!*1!*2!\right)
|
22,038 |
\dfrac{1}{\sqrt{z}} = z^{-\frac12}
|
3,361 |
(2 \cdot (-1) + 2^{10}) \cdot 6 = (2^{10} + 2 \cdot (-1)) \cdot {4 \choose 2}
|
-20,349 |
\dfrac{70}{-80} = -\dfrac{1}{8}\cdot 7\cdot (-\tfrac{1}{-10}\cdot 10)
|
9,127 |
133 + 3 \cdot (-1) + 117 \cdot (-1) = 13
|
32,671 |
12!/(6!\cdot 6!) = 924
|
19,217 |
\tfrac{4}{2\cdot i} = \frac2i = -2\cdot i
|
27,140 |
|a - x| + |x - c| = -(a - x) + x - c = -a + 2*x - c
|
23,125 |
y/y = 1 = \dfrac{y}{y}
|
-11,552 |
-i*17 - 6 + 5 = -17*i - 1
|
30,513 |
-x/(-2) = \frac{1}{-2} \cdot \left((-1) \cdot x\right) = x/2
|
-20,319 |
4/5\cdot (-\frac{1}{-9}\cdot 9) = -\frac{1}{-45}\cdot 36
|
48,252 |
(6 + 3 + 8 + 1)\cdot 3!\cdot 1111 = 119988
|
-6,745 |
6/100 + 4/10 = 6/100 + 40/100
|
242 |
(-\frac{1}{2} + 1)/2 = (\frac12)^2
|
14,912 |
|x| = \sqrt{x \cdot \overline{x}} = \sqrt{\overline{x} \cdot x} = |\overline{x}|
|
14,120 |
2 \cdot \left(2 \cdot a \cdot a + a \cdot 2 + 37\right) = \left(1 + 2 \cdot a\right)^2 + 73
|
-10,349 |
-9 = -f + 8 + 35 \cdot (-1) = -f + 27 \cdot (-1)
|
-23,106 |
-9/4 = -\dfrac12 3*\frac{3}{2}
|
-18,607 |
-\frac{20}{11} = -20/11
|
33,275 |
\dfrac{1}{2} \cdot 28 = 14
|
-12,396 |
\frac{1}{10.5}\times 21 = 2
|
1,777 |
x \cdot b + x^2 \cdot a = (a \cdot x + b) \cdot x
|
16,226 |
3! \cdot 6!/2! \cdot \binom{7}{2} \cdot \binom{2}{1} = 90720
|
-20,367 |
4/1\cdot \frac{9\cdot z}{9\cdot z}\cdot 1 = \frac{z\cdot 36}{9\cdot z}
|
17,017 |
(\cot{y} - \csc{y}) \cdot (1 + \cos{y}) = -\sin{y}
|
-25,223 |
n*z^{n + (-1)} = d/dz z^n
|
27,101 |
\frac{2\times x + 10}{x + 3} = \frac{1}{x + 3}\times (2\times (x + 3) + 4) = 2 + \dfrac{1}{x + 3}\times 4
|
25,330 |
30\%*y*80\% = 24\%*y
|
-1,207 |
1/3 \cdot 2/(\left(-7\right) \frac13) = \frac{1}{3}2 (-3/7)
|
-24,753 |
\cos(19\cdot π/12) = \frac{1}{4}\cdot (-\sqrt{2} + \sqrt{6})
|
-25,795 |
2/20 = 1\cdot 2/(5\cdot 4)
|
-1,469 |
((-7)\cdot 1/9)/((-5)\cdot \frac{1}{9}) = -7/9\cdot (-9/5)
|
-6,347 |
\frac{1}{r \times r + r\times 14 + 48}\times 2 = \frac{1}{(6 + r)\times (8 + r)}\times 2
|
5,246 |
\mathbb{E}(Y) = \mathbb{E}(\sum_{i=1}^n Y_i) = \sum_{i=1}^n \mathbb{E}(Y_i)
|
27,729 |
(a^2 - a*h + h^2)*(a + h) = a^3 + h^3
|
37,863 |
2\int \dfrac{1}{\sqrt{(z + \left(-1\right)) * (z + \left(-1\right))} \sqrt{z}}\sqrt{(z + (-1)) * (z + (-1))}\,dz = 2\int \frac{1}{\sqrt{z}}\,dz = 2\int z^{-0.5}\,dz
|
6,494 |
\dfrac{1}{1 + n}n = -\dfrac{1}{n + 1} + 1
|
6,031 |
(u + v)*(v^2 + u^2 - v*u) = u * u * u + v * v * v
|
13,503 |
0 = x + (-1) + y + 1 + z + \left(-1\right) \Rightarrow 1 = z + x + y
|
9,537 |
\sin\left(-e + x\right) = -\sin\left(e\right)\cdot \cos(x) + \cos(e)\cdot \sin(x)
|
41,595 |
1 + 2 + 3 = 1 \cdot 2 \cdot 3
|
28,596 |
|\mathrm{i} + 1| = \sqrt{2}
|
-4,419 |
\frac{1}{y^2 - 6*y + 5}*(11*\left(-1\right) - y) = -\frac{1}{5*(-1) + y}*4 + \frac{3}{(-1) + y}
|
9,394 |
(z*2 + y*5)*3 = z*6 + 15*y
|
16,851 |
-7\times 3^2 + 8^2 = 1
|
47,603 |
\binom{16}{8} = \tfrac{16!}{8!^2} = \frac{16\cdot 15\cdot 14\cdot 13\cdot 12\cdot 11\cdot 10\cdot 9}{8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2} = 12870
|
33,175 |
(9 \cdot 0 + 8 + 6 \cdot 2 + 0 \cdot 3 + 4)/4! = 1
|
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