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ddrg
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math_formulas

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-18,665
2\cdot n + 2 = 6\cdot \left(n + 3\right) = 6\cdot n + 18
-9,598
0.01 (-37) = -37.5/100 = -3/8
20,841
0 = c_1 - 1/2 + 5/2\Longrightarrow c_1 = -2
15,429
\left(u \cdot 3 - v\right)^2 + (-v + 3 \cdot u) \cdot (-u + v) - \left(v - u\right)^2 = -v^2 + 5 \cdot u^2
33,863
(1 + 1/n)^n*(1 - \frac{1}{n})^n = \left(1 - \frac{1}{n^2}\right)^n \gt 1 - \frac{1}{n}
14,491
\frac{2^9\cdot 66}{2^{12}} = 8.25
2,169
Y\cdot F\cdot t = t\cdot F\cdot Y
-4,797
1\cdot 10^4 = 1.0\cdot 10^{(-1)\cdot (-1) + 3}
-9,371
-n \times 2 \times 2 \times 2 = -8 \times n
7,970
\left((-1) + x\right)^3 = x \cdot x^2 - 1 + x \cdot 3 - 3 \cdot x \cdot x
22,539
s z - s \cdot 2 = 5 \left(-1\right) + 2 z + t \Rightarrow -s \cdot 2 - t + 5 = (s + 2 (-1)) z
28,472
|\rho_1| = |\rho_2| = q \Rightarrow q = |\rho_2\cdot \rho_1|
-22,768
36/60 = \frac{3}{5\cdot 12}\cdot 12
1,162
(2\cdot \left(5\cdot x + 2\right))^2 + 2\cdot (5\cdot x + 2) = 100\cdot x \cdot x + 80\cdot x + 16 + 10\cdot x + 4 = 10\cdot (10\cdot x^2 + 9\cdot x + 20)
31,502
\frac1y\times (y \times y + y) = 1 + y
8,356
-(-g + b) = g - b
-4,382
\frac{z^2}{z^5} = \frac{z \cdot z}{z \cdot z \cdot z \cdot z \cdot z} = \frac{1}{z^3}
25,121
2 - 9 \cdot y^7 + 7 \cdot y^9 = \left(1 - y\right)^2 \cdot (2 + 4 \cdot y + 6 \cdot y^2 + 8 \cdot y^3 + 10 \cdot y^4 + 12 \cdot y^5 + 14 \cdot y^6 + 7 \cdot y^7) \approx 63 \cdot (1 - y)^2
-1,738
\frac34*\pi = \pi*4/3 - \pi*\dfrac{7}{12}
18,795
l \cdot x^{l + \left(-1\right)} = \frac{\partial}{\partial x} x^l
20,353
5^2\cdot 6 \cdot 6\cdot 8\cdot 7 = 50400
32,071
60 = \dfrac{1}{2! \cdot 3!} 6!
-6,682
9/100 + \frac{1}{100}\times 20 = \frac{9}{100} + 2/10
-4,127
\frac18 \cdot 7 = \tfrac{7}{8}
-4,654
-\frac{1}{y + 2}3 - \frac{1}{y + 1}3 = \dfrac{-6y + 9(-1)}{y * y + 3y + 2}
23,623
367 \cdot (-1) + 3120 = 2753
3,751
y + 8 - 6*\sqrt{y + \left(-1\right)} = y + (-1) - 6*\sqrt{y + \left(-1\right)} + 9 = (\sqrt{y + \left(-1\right)} + 3*(-1))^2 = \left(3 - \sqrt{y + (-1)}\right)^2
44,277
\left(4^2\cdot 8 - 2^2\cdot 2\cdot 3\right)\cdot \frac{\pi}{3} = \pi\cdot 104/3
34,879
(a - x)/4 = -x/4 + \frac{1}{4} \cdot a
6,313
t + q + (-1) = -((-1) + q) \cdot (\left(-1\right) + t) + q \cdot t
12,046
\frac{76!}{76! - 75!} = \dfrac{76*75!}{75! (76 + (-1))} = 76/75
21,419
16 = (3 + 1) \cdot (3 + 1)
231
x\cdot 2 + \omega = \frac{1}{\omega}\cdot ((x + \omega) \cdot (x + \omega) - x^2)
22,585
h^{f \cdot g} = (h^f)^g = (h^g)^f
-22,907
5*3/(5*5) = \frac{15}{25}
8,283
a \cdot b = \frac{1}{\dfrac{1}{a \cdot b}} = \tfrac{1}{1/a \cdot \frac1b} = \frac{1}{\frac{1}{b} \cdot 1/a} = b \cdot a
15,516
e^y*e^x = e^{x + y}
25,872
0 = w\cdot u\cdot w = w\cdot \left(c\cdot u + b\cdot w\right) = c\cdot u\cdot w + b\cdot |w|^2
27,057
\frac{1}{e^{(-1) \times \left((-2) \times 1.0 \times 10^{-10}\right) \times 1000}} \times 2 = 2 \times 0.999999 = 1.99999
52
\dfrac{x}{40}\cdot 40 = x\cdot \frac{1}{40}\cdot 40 = x = x
19,857
\alpha * \alpha \beta^2 = \alpha^2 \beta * \beta
-6,928
24 = 2*4*3
18,416
\sin(4\left(y + \pi\right)) = \sin(y*4)
3,571
1 + \alpha^4 = 1 + 2\cdot \alpha^2 + \alpha^4 - 2\cdot \alpha \cdot \alpha = (1 + \alpha^2)^2 - (\sqrt{2}\cdot \alpha)^2
35,503
\frac{1}{1 + x^2}\cdot \left(x^6 + 1\right) = x^4 - x^2 + 1
-11,742
(\frac198)^2 = 64/81
11,884
1 + y + 2*y^2 + 3*y^3 + \cdots = 1 + \frac{1}{(-y + 1)^2}*y
15,413
\binom{x_1 + x_2}{x_1} = \frac{1}{x_1! \cdot x_2!} \cdot (x_1 + x_2)!
19,664
b_n^{m + (-1)}\cdot b_{(-1) + n}\cdot a_m\cdot m = a_m\cdot b_{n + (-1)}\cdot b_n^{\left(-1\right) + m}\cdot {m \choose 1}
-9,188
-24*i + 20 = -2*2*2*3*i + 2*2*5
18,132
|\Re{(x)}| \leq |x|\Longrightarrow 0 \leq -\left(\Re{(x)}\right)^2 + |x|^2
-18,385
\frac{a\times (a + 6)}{(a + 7\times (-1))\times \left(6 + a\right)} = \frac{1}{a^2 - a + 42\times (-1)}\times (a^2 + 6\times a)
3,339
\mathbb{E}\left[Bv\right] = B^2 v = Bv = Bv
17,214
4^2/12 = 16/12 = 4/3
19,950
J\cdot 3\cdot i = i\cdot 3\cdot J
-17,720
10 = 12 + 2*(-1)
23,971
\frac{-X^{m + 1} + 1}{-X + 1} = 1 + X + X \cdot X + ... + X^m
15,760
\frac{1}{2} = \dfrac{1}{24}\cdot 12
20,999
\sqrt{z}\cdot e^{z\cdot 3} = \frac{\sqrt{z}}{e^{-z\cdot 3}}
204
x \cdot x \cdot 9 = (x \cdot 3) \cdot (x \cdot 3)
-20,311
\tfrac{1}{7}*(x + 4)*\frac{1}{5}*5 = \frac{1}{35}*\left(20 + x*5\right)
11,002
1 + y + y^2 + \dots = \dfrac{1}{-y + 1}
-8,428
8 = \left(-1\right)\cdot (-8)
17,118
\left(k + (-1)\right)\cdot \left(k + 1\right) = k^2 + (-1)
-16,026
46/10 = 10\cdot 7/10 - 8\cdot \frac{1}{10}3
33,866
K \cdot 9 = K \cdot 25 = K
2,136
z^4 - N^4 = (z^2 + N * N) (z^2 - N^2)
6,311
\sin(v+w) = \sin(v)\cos(w)+\cos(v)\sin(w)
1,678
(p - z*2) * (p - z*2) = p^2 - 4*p*z + 4*z^2
17,071
\dfrac{1}{2 \left(-1\right) + 1} = -1
19,964
x^2 + x^2 + 1 = x x + x + x + x x = x^2 + x + x + x^2 + 1
28,232
\left(z^m + a^m \Leftrightarrow a + z = 0\right) \Rightarrow 0 = z^m + a^m
-11,613
0 + 20*(-1) + i*20 = -20 + 20*i
19,922
40/7 = 5 + \tfrac{5}{7}
20,302
n!/i! = {n \choose i}*\left(n - i\right)!
1,310
\frac{1}{x + \left(-1\right)} \cdot (x \cdot x + (-1)) = \frac{1}{x + \left(-1\right)} \cdot \left(x + 1\right) \cdot \left(x + \left(-1\right)\right) = x + 1
4,216
c^2\cdot d = d = d\cdot c \cdot c
7,670
-(i + (-1)) + k + 2\cdot (-1) = k + 2\cdot \left(-1\right) - i + 1
41,341
-\sin(z) = \sin\left(\pi + z\right)
5,288
1 + 3 + \cdots + 2 \cdot n + (-1) + 2 \cdot (n + 1) + (-1) = n^2 + 2 \cdot n + 1 = (n + 1) \cdot (n + 1)
-2,444
(2 + 3 + 4)\times \sqrt{7} = 9\times \sqrt{7}
-4,482
(2*(-1) + x)*(3*(-1) + x) = x^2 - 5*x + 6
-6,132
\frac{1}{2*\varphi + 20*\left(-1\right)}*3 = \frac{1}{2*(10*(-1) + \varphi)}*3
31,397
x/x = x\cdot x/x/x = (\frac{x}{x})^2
16,663
{6 \choose 3}*{3 \choose 2}*{2 \choose 1}*{3 \choose 1} = 6*5*4*3
9,936
(8 + 1)\cdot (1 + 4)\cdot (1 + 1)\cdot (1 + 1)\cdot \left(1 + 1\right) = 360
12,312
d\cdot x\cdot E^2 = d\cdot E^2\cdot x
-16,360
8*16^{1 / 2}*5^{1 / 2} = 8*4*5^{\dfrac{1}{2}} = 32*5^{1 / 2}
23,222
a^U \cdot x^l = x^l \cdot a^U
23,424
10 = (1 + 1)\cdot (1 + 4)
11,103
(10 + (-1))/3 = (18 + 3\cdot (-1))/5 = \left(2 + 26\cdot (-1)\right)/(-8)
15,745
B \cdot Y = x\Longrightarrow x = B \cdot Y
28,296
\overline{M} + \overline{z} = \overline{M + z}
9,485
4^k \frac{2}{k + 2} = \frac{1}{k + 2} 2^{1 + k\cdot 2}
-5,904
\dfrac{5}{(p + 3\times (-1))\times (p + 2\times (-1))} = \frac{5}{6 + p \times p - p\times 5}
8,946
2^{1 + k} + 2*(-1) = (2^k + (-1))*2
13,260
(y^6)^{36} + \left(-1\right) = \left(-1\right) + y^{216}
-22,294
(7 (-1) + a) (9 (-1) + a) = a^2 - 16 a + 63
7,006
4 + x^2 - 4*x = \left(x + 2*(-1)\right)^2
-1,951
-π/6 + \frac{π}{12} = -π/12