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17,102 | (a - b) \cdot (a - b) = b \cdot b + a \cdot a - 2\cdot a\cdot b |
20,075 | x + (-1) = x + 2\cdot (-1) + 1 |
14,258 | \left(2*m + 3\right)*m + 1 = 2*m * m + 3*m + 1 = (2*m + 1)*\left(m + 1\right) |
-4,565 | x^2 + x*5 + 6 = (2 + x) (x + 3) |
41,381 | 1*23 + 4(-1) + 5 + 6(-1) + 7(-1) = 11 |
38,448 | \sin{z} = \cos(-\frac{1}{2}\cdot \pi + z) |
9,859 | T - X \lt X \Rightarrow T \lt 2 X |
-7,956 | \dfrac{-2 - i}{-i - 2}\times \dfrac{1}{-2 + i}\times \left(i + 8\right) = \frac{1}{i - 2}\times \left(8 + i\right) |
8,351 | \frac{h}{d} + x/d = \frac1d \cdot \left(h + x\right) |
38,583 | 64232 = 39 * 39^2 + 17^3 |
-20,186 | -4/7*9/9 = -36/63 |
778 | \dfrac{8(-1) + 120}{5 + (-1)} = 28 |
26,596 | 2 + x^2 - x*3 = (\left(-1\right) + x)*\left(2*(-1) + x\right) |
21,531 | \frac{1}{y \cdot y + 1}\cdot y^2 = \frac{y^2 + 1 + (-1)}{y \cdot y + 1} = 1 - \dfrac{1}{y^2 + 1} |
-20,435 | \frac{4*(-1) + s}{s*7 + (-1)}*\dfrac14*4 = \dfrac{16*(-1) + s*4}{s*28 + 4*(-1)} |
-19,720 | 6\cdot 6/(7) = \frac{1}{7}\cdot 36 |
5,096 | N*2^{N + (-1)} = \dfrac{2^{N + (-1)}}{(-1) + 2^N}N*((-1) + 2^N) |
17,632 | \mathbb{E}\left[B_1 + B_2 + B_3\right] = \mathbb{E}\left[B_3\right] + \mathbb{E}\left[B_1\right] + \mathbb{E}\left[B_2\right] |
5,219 | \left(A + 2*\left(-1\right)\right)*(A + 1) = 2*(-1) + A^2 - A |
21,205 | \frac{1}{k^{1/2} + (k + 1)^{1/2}} = \left(1 + k\right)^{1/2} - k^{1/2} |
-13,343 | \dfrac{12}{9 + 3\cdot (-1)} = \dfrac{12}{6} = 12/6 = 2 |
-30,263 | (y + 7)\cdot (y + 7\cdot (-1)) = y^2 + 49\cdot (-1) |
30,303 | \mathbb{E}\left[X\right] \cdot \mathbb{E}\left[B\right] = \mathbb{E}\left[X \cdot B\right] |
29,319 | a^x*\ln(a) = \frac{\partial}{\partial x} a^x |
12,339 | n = \left\{\dotsm, 1, n\right\} |
-4,244 | \frac{63 \cdot n}{n^5 \cdot 54} \cdot 1 = 63/54 \cdot \dfrac{1}{n^5} \cdot n |
4,421 | \left(r + (-1)\right) (1 + r^2 + r) = r^3 + \left(-1\right) |
21,904 | E\left(A\right)\cdot E\left(H\right) = E\left(H\cdot A\right) |
20,156 | u_x + f\cdot u_y = 0 = \left( 1, f\right)\cdot ( u_x, u_y) |
1,858 | \|t - r\|^2 = \|t - x + x - r\|^2 = \|t - x\|^2 + \|x - r\|^2 + 2 |
-4,884 | 10^{1 + 3}*15 = 15*10^4 |
5,927 | ((-1) + z^2) \cdot \left(1 + z^4 + z^2\right) = (-1) + z^6 |
16,587 | (x + 0) \left(x^2 + 2x + 2\right) = 0 + x^3 + 2x^2 + 2x |
14,449 | 0 = (-1) + 4\cdot x \Rightarrow 1/4 = x |
24,934 | \frac{\partial}{\partial x} x^{\tfrac{1}{q}} = \tfrac1q\times x^{(1 - q)/q} = \tfrac{1}{q}\times x^{1/q + (-1)} |
4,685 | -8 \geq \frac6y \implies y \geq -6/8 = -3/4 |
23,766 | y^{\frac1e} = y^{1/e} |
2,616 | \frac{1}{6^3}(6 + 54 + 18) = 78/216 = \frac{13}{36} \approx 0.361 |
31,877 | 212/39 = \frac{1}{39}17 + 5 |
-1,116 | -40/42 = ((-40) \dfrac{1}{2})/\left(42*1/2\right) = -20/21 |
11,137 | c_1^{c_2}\cdot c_1^d = c_1^{c_2 + d} |
2,270 | x^2 - z^2 = x*x - z*z = \left(x + z\right)*\left(x - z\right) |
-8,506 | \frac{1}{-9} \cdot 9 = -1 |
9,301 | AG_{11} = G_{11} A |
16,663 | \binom{2}{1} \binom{3}{1} \binom{3}{2} \binom{6}{3} = 6*5*4*3 |
21,829 | \left(n = 6 \Leftrightarrow 2 + n = 8, 4 n + 1 = 25\right) \implies \left( 2 + n, 1 + 4 n\right) = 1 |
28,545 | 2 = 1 - 2 + 3*(-1) |
10,273 | \dfrac12 = (-1) - 1 + \frac{1}{2} + 2 |
22,112 | 2\times \cos{z} = e^{i\times z} + e^{-i\times z} = e^{i\times z} + e^{-i\times z} = 2\times \cosh{i\times z} |
26,599 | \tfrac12\cdot \left(\cos(x\cdot 2) + 1\right) = \cos^2\left(x\right) |
-8,085 | \frac{1}{i\cdot 5 + 3}\cdot (2 - 8\cdot i) = \dfrac{1}{i\cdot 5 + 3}\cdot (2 - i\cdot 8)\cdot \frac{3 - 5\cdot i}{3 - i\cdot 5} |
34,360 | -p + p^3 + p^2 = (-1) + p^2 + p^2 - p + p^2 - p + p^2 - p \cdot 2 + 1 + p^3 - 3 \cdot p^2 + p \cdot 3 |
8,979 | 20538 = 2 \cdot 3^2 \cdot 7 \cdot 163 |
8,745 | c = a \Rightarrow a^2 = c^2 |
13,321 | -\frac{1}{2 + x^2} + 1 = \dfrac{1 + x^2}{x^2 + 2} |
11,601 | (n + \left(-1\right))!\cdot (n + 1)! = (n + 1)/n\cdot n!^2 > n!^2 |
31,858 | 12\cdot (-1) + 6 = -6 |
29,602 | \sin(\alpha + \frac{\pi\cdot 3}{2}) = -\cos\left(\alpha\right) |
27,725 | |A \cap F| = |A \cap F| |
48,776 | 2^1*5 + 1 = 11 |
29,115 | c + 3\cdot z\cdot b = 0 \Rightarrow -\frac{c}{b\cdot 3} = z |
6,473 | \frac{1 + 2 \cdot z}{2 + 2 \cdot k} = \dfrac{1}{2} \cdot \left(\dfrac{z + 1}{k + 1} + \dfrac{z}{k + 1}\right) |
-11,971 | 71/90 = p/(12*\pi)*12*\pi = p |
32,210 | \binom{2 + k}{1 + k} = 1 + \binom{k + 1}{k} |
24,502 | -l^2 + x^2 = (l + x) (-l + x) |
32,384 | 15\times3=45 |
-1,858 | \pi \cdot \frac{13}{12} = \dfrac{1}{4} \cdot 3 \cdot \pi + \frac{\pi}{3} |
-5,742 | \frac{5*p}{8 + p^2 - p*9} = \tfrac{1}{(p + 8*(-1))*((-1) + p)}*5*p |
12,973 | a + z - a = a + y - a \Rightarrow -a + a + z = y - a + a |
-20,802 | 4/1 \cdot \frac{9 + 10 \cdot k}{9 + k \cdot 10} = \frac{40 \cdot k + 36}{10 \cdot k + 9} |
-29,357 | (2 + Y)*(2 - Y) = 2^2 - Y^2 = 4 - Y^2 |
10,999 | \int (1 - e^{-z}) \cdot e^{e^z}\,dz = \int (e^z + \left(-1\right)) \cdot e^{-z} \cdot e^{e^z}\,dz = \int \left(e^z + (-1)\right) \cdot e^{e^z - z}\,dz |
-2,188 | -3/12 + \dfrac{7}{12} = 4/12 |
13,956 | f_1 \cdot z_0 + z_1 = z_1 + z_0 \cdot f_1 |
31,804 | c*b*a = (a + i)*10 * 10 + b*10 + c - i = a*10^2 + b*10 + c + i*10^2 - i = a*10 * 10 + b*10 + c + 99*i |
-3,118 | 12 \cdot 2^{1/2} = 2^{1/2} \cdot (4 + 3 + 5) |
3,389 | 1/4 + 1/3 + 1/2 = \frac{13}{12} |
19,879 | 6^2*4 = 4^2 + 8^2 + 8 * 8 |
4,522 | \frac{1}{29}\cdot 9 = 9/29 |
24,957 | y^{a - h} = \frac{y^a}{y^h} |
12,863 | -6 = \sqrt{2} + 3*(-1) - \sqrt{2} + 3*\left(-1\right) |
45,656 | (\sqrt{c})^2 + (\frac{1}{\sqrt{c}})^2 + 2 = (\sqrt{c} + \frac{1}{\sqrt{c}}) \cdot (\sqrt{c} + \frac{1}{\sqrt{c}}) = \left(c + 1\right)^2/c |
-6,667 | \dfrac{5}{3x + 12 (-1)} = \tfrac{5}{3(4(-1) + x)} |
35,084 | \cos{\alpha} \sin{\alpha}\cdot 2 = \sin{2\alpha} |
30,489 | z + 3 < 0 \implies -3 \gt z |
8,777 | a^2 \cdot a + b^3 + c^3 - 3\cdot a\cdot b\cdot c = (c + a + b)\cdot (a^2 + b^2 + c^2 - a\cdot b - c\cdot b - a\cdot c) |
28,667 | k + (-1) = j \Rightarrow k = j + 1 |
19,648 | (-\mathrm{i} + 1) (\mathrm{i} + 1) = 2 |
10,772 | -2x + x \cdot x = (-1) + ((-1) + x)^2 |
7,571 | 60 (-1) + 1024 + 4 (-1) = 960 |
-4,459 | x \cdot x + 3 \cdot x + 10 \cdot (-1) = \left(x + 5\right) \cdot (2 \cdot (-1) + x) |
-20,557 | \frac{1}{(-5)*y}*\left((-1) - 9*y\right)*\frac12*2 = (-y*18 + 2*(-1))/(\left(-10\right)*y) |
-18,274 | \frac{-g\cdot 5 + g \cdot g}{g^2 + 4\cdot g + 45\cdot \left(-1\right)} = \frac{1}{(g + 5\cdot \left(-1\right))\cdot (9 + g)}\cdot g\cdot \left(5\cdot (-1) + g\right) |
52,970 | \int\frac{x^2}{\tan{x}-x}dx=\int\left(\frac{x^2}{\tan{x}-x}+x-x\right)dx=\int\frac{x\sin{x}}{\sin{x}-x\cos{x}}dx-\frac{x^2}{2} |
16,445 | A^{\frac12}\cdot A^{1/2} = A |
13,491 | v_3\cdot v_1\cdot v_2 = v_3\cdot v_1\cdot v_2 |
409 | 4y = y \cdot 2 \cdot 2 |
13,375 | (r + 1)/2 = r - \dfrac{1}{2}\cdot ((-1) + r) |
4,874 | 2^{\frac{1}{3} \cdot (m + 1)} = 2^{1/3} \cdot 2^{m/3} > m \cdot 2^{\dfrac{1}{3}} |
15,052 | -\binom{10}{1} + 2^{10} + (-1) = 2^{10} + 11 \times (-1) |
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