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ddrg
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math_formulas

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21,660
-x^3 + 1 = (x \times x + 1 + x) \times \left(1 - x\right)
12,266
\cos^2{t} = \frac{1}{2}\times \left(\cos{2\times t} + 1\right)
4,157
\sec\left(π/2 - x\right) = \csc{x}
1,669
(f, b) = f\cdot b/(b\cdot f) = \frac{f}{f}\cdot 1
15,746
k! = k\cdot (k + (-1))\cdot ...\cdot 2
9,112
\frac{x}{2 \cdot \pi} = x/2 \cdot \pi = \frac{\pi}{2} \cdot x
4,546
|X \cdot T| = |T| \cdot |X|
-11,590
-12 - 9 \cdot i = 0 + 12 \cdot (-1) - i \cdot 9
-17,009
3 = 3(-r) + 3(-5) = -3r - 15 = -3r + 15 (-1)
-8,767
9 \cdot 9 \cdot 9 = 729
32,740
\frac{1}{\left(-1\right) + \sqrt{3}} = \dfrac{1}{2} \cdot (1 + \sqrt{3})
21,413
(1 - z^{1/2}) (z^{1/2} + 1) = 1 - z
1,606
a^{b + (-1)} = \frac{1}{a}\times a^b
17,519
(y + x) * (y + x) = y^2 + x^2 + y*x*2
1,093
-m^3 + (m + 1)^3 = 3 \cdot m^2 + m \cdot 3 + 1
-4,049
\frac{3*y^2}{2} = y^2*\dfrac{3}{2}
12,869
\left(b^3 = x^3\Longrightarrow x^9 = b^9\right)\Longrightarrow x^2 = b^2
13,321
\frac{x^2 + 1}{2 + x^2} = 1 - \dfrac{1}{2 + x^2}
28,830
\tfrac{1}{t_i - t_j}\cdot (1/(t_i) - 1/(t_j)) = -\frac{1}{t_j\cdot t_i}
-5,380
\tfrac{1}{100}\times 44.1 = 44.1/100
-7,015
3/9\cdot 2/8 = 1/12
20,767
\frac{x}{100} \cdot y = x \cdot y/100
-20,126
\dfrac{1}{3 \cdot k + 6} \cdot (k \cdot 24 + 27 \cdot (-1)) = 3/3 \cdot \dfrac{1}{2 + k} \cdot (9 \cdot (-1) + 8 \cdot k)
8,199
z^2 + 2*z + 25 = 24 + (z + 1) * (z + 1)
-20,286
-\dfrac{30}{21} = 3/3\cdot (-\frac{10}{7})
11,446
x = \frac{1}{\pi} \cdot \pi \cdot x
32,208
z^2 - 4\cdot z + 120 = z^2 - 4\cdot z + 4 + 116 = \left(z + 2\cdot (-1)\right) \cdot \left(z + 2\cdot (-1)\right) + 116
23,280
a^Y \cdot x \cdot a = a \cdot x \cdot a^Y
30,613
2^{m + 1} + 2*(-1) = 2^1*2^m + 2*(-1) = 2*\left(2^m + \left(-1\right)\right)
29,975
4200 = \frac{10!}{4! \times 3! \times 3!}
11,396
5 \times 2^1/2 = 20/4
22,109
\frac{d}{h} = \frac{d}{h}
-20,339
\frac{1}{2}\cdot 9\cdot (-4/(-4)) = -36/(-8)
9,011
\frac{1}{\cos(\sin^{-1}(x))} = d/dx \sin^{-1}\left(x\right)
443
b_{1 + x} = (1 + b_x) \times (x + 1) rightarrow x + 1 = \frac{b_{1 + x}}{b_x + 1}
-5,464
\dfrac{3 \cdot n}{n^2 + 25 \cdot (-1)} \cdot 1 = \frac{3 \cdot n}{(5 + n) \cdot (n + 5 \cdot (-1))}
-4,854
9.1 \cdot 10^3 = 9.1 \cdot 10^{5 \cdot (-1) + 8}
6,609
(z + 1)^5 = \left(z^4 + 1\right)*\left(z + 1\right) = z^5 + z^4 + z + 1
-27,690
\sin{y} \cdot 9 = d/dy (-9 \cdot \cos{y})
27,152
\frac{1}{2} = \tfrac{1}{2 \cdot 2} + \frac{1}{2 \cdot 2}
26,988
n^{\frac{1}{2}}*(n^{\frac{1}{2}} + 2*\left(-1\right)) = -2*n^{\frac{1}{2}} + n
-19,047
\frac15 = \dfrac{A_s}{100 \cdot \pi} \cdot 100 \cdot \pi = A_s
30,640
f^2\cdot f\cdot f^2 = f^5
27,502
\left(-1\right) + x^2 = (x + (-1))*(1 + x)
5,303
r^2 + z^2 = r^2 + z \cdot z + 2\cdot r\cdot z - 2\cdot r\cdot z = \left(r + z\right)^2 - 2\cdot r\cdot z
13,220
\left(\sqrt{17} \gt 4 \Rightarrow -\sqrt{17} - 1 < -5\right) \Rightarrow (-1 - \sqrt{17})/4 < -1
28,451
|b| = 5 \implies |b^3| = 5
-7,296
\frac{1}{16}5 = \frac{5\cdot \frac{1}{8}}{2}
-25,231
\frac{\mathrm{d}}{\mathrm{d}x} \sqrt{x^3} = 3/2\cdot x
2,355
\sqrt{x + x * x - 3*x + 1}*2 + 1 = 2*\sqrt{1 + x^2 - 2*x} + 1
-9,301
-n\cdot 2\cdot 3\cdot 7\cdot n\cdot n = -42\cdot n^3
-7,108
\frac{1}{35}6 = 6/15*\frac{6}{14}
15,204
(k + t - t)^{k + t} = k^{k + t}
3,312
\mathbb{E}(a + bB) = \mathbb{E}(a) + \mathbb{E}(bB) = a + b\mathbb{E}(B)
-16,824
{7x} = ({7x} \times -2x) + ({7x} \times -1) = (-14x^{2}) + (-7x) = -14x^{2} - 7x
16,866
\frac{1}{24^2} \cdot 6^4 = \frac94
-20,017
\frac{1}{-14} \cdot (42 \cdot \left(-1\right) + 7 \cdot a) = \frac{1}{-2} \cdot \left(a + 6 \cdot (-1)\right) \cdot \dfrac17 \cdot 7
26,237
\sin{l\cdot 2} = \cos{l}\cdot \sin{l}\cdot 2
19,869
k_r = \sqrt{-k_r^2 + 1}
20,042
b = b^1 = b^{p m + x n} = (b^m)^p \cdot (b^n)^x
-16,592
10*\sqrt{52} = \sqrt{4*13}*10
-12,131
9/20 = \frac{1}{10 \cdot \pi} \cdot t \cdot 10 \cdot \pi = t
4,542
\frac{z + 0*(-1)}{0*(-1) + x} = z/x
12,481
97 = \frac{1}{2 + (-1)} \cdot (3 \cdot (-1) + 100)
20,927
-g \cdot d = 1 \implies -1/d = g
49,220
4 = \frac13 \times 12
30,007
5*18/5/2 = 9
-24,687
4 + 14 \times \left(-4 \times i\right) = 4 + 14 \times (-4 \times i) = 18 \times (-4 \times i)
26,396
\frac{y}{y^2 - 4\cdot y + 4 + 4} = \tfrac{y}{(y + 2\cdot (-1))^2 + 4} = \frac{y}{(y + 2\cdot \left(-1\right))^2 + 2^2}
5,050
y^3 - 23 y^2 + 142 y + 120 (-1) = y^3 - y^2 - y^2\cdot 22 + y\cdot 22 + y\cdot 120 + 120 \left(-1\right)
17,009
A \times G = A \times G
36,001
1/(F\cdot Y) = 1/(Y\cdot F)
-29,020
z^{l + k} = z^l z^k
19,159
a^3 + 1 = (a + 1)*(a^2 - a + 1)
19,745
\frac{2}{24} = 1/6\cdot 1/12\cdot 6
-26,592
x^2\cdot 25 + 16\cdot (-1) = (x\cdot 5 + 4)\cdot (4\cdot (-1) + 5\cdot x)
-2,245
4/11 = -\frac{1}{11} + \frac{5}{11}
-26,309
3 = G \cdot e^{(-7) \cdot 0} = G
28,343
(1 + 3444)/5 = 689
-18,057
40 = 71 + 31 \left(-1\right)
3,980
1 = (x + \dfrac{1}{x})^5 = x^5 + \dfrac{1}{x^5} + 5\cdot (x^3 + \frac{1}{x^3}) + 10\cdot (x + 1/x)
-2,824
6^{\frac{1}{2}} \times 10 = 6^{1 / 2} \times (4 + 5 + 1)
6,154
az^{a + \left(-1\right)} = \frac{\partial}{\partial z} z^a
-22,381
24\cdot (-1) + A^2 + A\cdot 2 = (6 + A)\cdot (A + 4\cdot (-1))
20,909
(\cos{-\pi} + i*\sin{-\pi})*8 = -8
13,683
1 = \dfrac{a + b}{a + b} = \frac{a}{a + b} + \frac{b}{a + b}
25,291
E^m = \left(-3\right)^{m + (-1)} E = -\frac{(-3)^m E}{3}
25,772
\sin^2(x) - \cos\left(x\right)*(1 - \cos(x)) = \sin^2(x) + \cos^2(x) - \cos(x) = 1 - \cos\left(x\right)
4,298
b + e = 0 \implies -e = b
7,508
v\cdot (A + H) = A\cdot v + H\cdot v
15,073
1 = \frac{1}{2 + 2}*(2 + 2) = \dfrac{2}{2} + \tfrac12*2 = 2
27,048
12/17\cdot \dfrac23 = \frac{1}{17}\cdot 8
26,038
\pi + \frac{\pi\cdot 3}{8}\cdot 1 = \pi\cdot 11/8
22,454
a^2 - 2*c*a + c^2 = \left(a - c\right) * \left(a - c\right)
-4,427
-\frac{3}{x + 1} - \frac{1}{2 + x}*2 = \frac{8*(-1) - 5*x}{x^2 + x*3 + 2}
28,503
65 = (2^2 + 1^2) (3^2 + 2^2) = 8 8 + 1^2 = 4^2 + 7^2
17,843
\frac{9}{9^2 + 11 (-1)}*8/9 = \frac{4}{35} \approx 0.114285714285714
15,676
x^{\tfrac16}*x^{1/3} = x^{1/6}*x^{1/3} = \sqrt{x}
30,060
\left(x^2\right)^m = e \Rightarrow e = x^{m\cdot 2}
21,124
s*\sqrt{2} - s = s*\sqrt{2} - p*\sqrt{2} = \left(s - p\right)*\sqrt{2}