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ddrg
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math_formulas

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39,123
(h + b)^2 = h^2 + 2*h*b + b^2 \geq h^2 + b^2
9,011
\frac{\mathrm{d}}{\mathrm{d}z} \operatorname{asin}\left(z\right) = \frac{1}{\cos\left(\operatorname{asin}(z)\right)}
-1,769
π \cdot 13/12 + 3/4 \cdot π = π \cdot 11/6
10,972
4 = (a + f)^2 = a \cdot a + f^2 + 2\cdot a\cdot f
-6,303
\frac{1}{q*3 + 27} = \frac{1}{(q + 9)*3}
13,481
\dfrac{5!}{2! \cdot 2! \cdot 1!} = \frac{120}{4} = 30
20,408
(g^2 + f^2) \cdot (x^2 + h^2) = (g \cdot x + f \cdot h)^2 + (g \cdot h - f \cdot x) \cdot (g \cdot h - f \cdot x) = (g \cdot x - f \cdot h) \cdot (g \cdot x - f \cdot h) + \left(g \cdot h + f \cdot x\right)^2
-4,780
\frac{1}{5 + y^2 + y\cdot 6}\cdot (9\cdot (-1) - y) = -\frac{1}{1 + y}\cdot 2 + \frac{1}{5 + y}
14,531
-((-1) + x)^2 + (x + 1)^2 = 4*x
17,661
2^4 = (\sqrt{-7} + 1)^4 + (1 - \sqrt{-7})^4
24,127
4500 = \dfrac{1}{2}*\left(9999 + 1000*(-1) + 1\right)
8,617
2(a^2 + b^2 + c^2 + (-1)) = 2(a^2 + b^2 + c^2 - ab - bc - ac) = (a - b) * (a - b) + \left(b - c\right)^2 + (c - a) * (c - a)
20,491
\frac{1}{2^{(-1) + m}} = \frac{1}{2^m \cdot 1/2}
14,634
\frac{a*1/b}{c} = \dfrac{a}{c*b}
2,878
2\cdot f_1\cdot f_2 + 8 = f_2^3 - f_1^3 = \left(f_2 - f_1\right)\cdot (f_2 \cdot f_2 + f_2\cdot f_1 + f_1 \cdot f_1) \geq 2\cdot (f_2 \cdot f_2 + f_2\cdot f_1 + f_1 \cdot f_1)
6,034
-x^2 + y * y - x^3 = \left(y + x*\left(x + 1\right)^{1 / 2}\right) (y - \left(1 + x\right)^{\dfrac{1}{2}} x)
28,177
|x + (-1)| = |x + \left(-1\right) + 0*(-1)| \leq |x + (-1)| + 0
27,379
2\cdot x\cdot 2 = x\cdot 4
25,300
4\cdot 5/(1\cdot 2) = 10
-20,507
\frac{j \cdot 3 + 21}{j \cdot 10 + 70} = 3/10 \cdot \frac{1}{7 + j} \cdot (7 + j)
23,430
b^{1/2}\cdot a^{1/2} = b^{1/2}\cdot a^{1/2}
9,936
(1 + 1)\cdot \left(1 + 1\right)\cdot (1 + 1)\cdot (1 + 4)\cdot (1 + 8) = 360
-26,534
(100 + x^2 - x\cdot 20)\cdot 2 = 200 + x^2\cdot 2 - x\cdot 40
23,216
|f \cdot c| = |c| \cdot |f|
2,090
n^a\times n^b = n^{a + b}
-11,487
i\cdot 6 = i\cdot 6 + 0 + 0\cdot (-1)
861
3^n = 3^{n + \left(-1\right)} \cdot 3 \gt (n + (-1)) \cdot 3 = 3 n + 3 (-1) \gt n
8,329
-\pi/2 - 1 = -1 + (\left(-1\right)\cdot \pi)/2
35,139
i*x*2 + x^2 = 0 \Rightarrow x
-4,581
\dfrac{-2x-5}{x^2+9x+20} = \dfrac{-5}{x+5} + \dfrac{3}{x+4}
-4,416
x^2+4x-5 = (x+5)(x-1)
-20,930
-8/5 \frac{(-5) x}{\left(-5\right) x} = x\cdot 40/((-25) x)
23,085
\binom{2}{2}\cdot \binom{4}{2}\cdot \binom{6}{2} = 90
-23,428
\frac{1}{4} \cdot 3/5 = 3/20
-22,242
(3 + s)\cdot (s + 9\cdot (-1)) = 27\cdot (-1) + s \cdot s - 6\cdot s
-13,332
8 + \frac{1}{10}30 = 8 + 3 = 11
2,834
T \cdot r \cdot r = (r \cdot T + s) \cdot r = r \cdot (r \cdot T + s) + s \cdot r = r^2 \cdot T + 2 \cdot r \cdot s
12,032
\left(z + (-1)\right)^{1/2} = \left(z + \left(-1\right)\right)^{1/2} \neq (z + (-1))^{-1/2}
25,866
2016 = 3^2*7*2^5
7,460
2 + 2/3 \cdot (2 \cdot \left(-1\right) + 5) = 4
31,825
-\cos(x) = -\cos(-x)
-3,561
\frac{r \cdot 6}{12 \cdot r^2} = \frac{r}{r^2} \cdot \frac{1}{12} \cdot 6
-3
-19 = 4\cdot (-1) - 15
8,710
1 + i^5\cdot 6 + i^4\cdot 15 + 20\cdot i^3 + i^2\cdot 15 + i\cdot 6 = \left(i + 1\right)^6 - i^6
-18,353
\frac{n}{(6 + n) (n + 5 (-1))} (n + 6) = \frac{6 n + n^2}{n^2 + n + 30 \left(-1\right)}
-13,536
7 + 7\cdot 3 = 7 + 21 = 7 + 21 = 28
-747
(e^{i\pi})^{11} = e^{i\pi*11}
28,274
{i + j \choose i} = \dfrac{1}{j! \cdot i!} \cdot (i + j)!
8,416
1 = \frac{1}{1 - \frac{1}{6}5}c = \frac{c}{\frac16}
-15,567
\dfrac{h^{10}}{\frac{1}{z^2}\cdot h^5}\cdot \dfrac{1}{z^8} = \dfrac{(\frac{h^5}{z^4})^2}{\frac{1}{z^2\cdot \frac{1}{h^5}}}
-7,698
\frac{1}{10}(7 + 11 i - 21 i + 33) = (40 - 10 i)/10 = 4 - i
20,312
{n + (-1) \choose k + (-1)}*\frac{n}{k} = {n \choose k}
13,077
\cos(2\cdot p) = x \Rightarrow -\sin\left(2\cdot p\right)\cdot 2 = \frac{\text{d}x}{\text{d}p}
21,063
\frac{1}{2} \cdot 6 + \dfrac{1}{3} \cdot 5 + \frac16 \cdot 4 = 16/3
14,930
h^d = h^{2 \cdot \dfrac{d}{2}} = (h^2)^{d/2}
-20,230
\frac{1}{-t \cdot 4 + 3 \cdot (-1)} \cdot 3 \cdot 5/5 = \frac{15}{15 \cdot (-1) - 20 \cdot t}
-24,089
\frac{32}{6 + 10} = 32/16 = 32/16 = 2
8,903
\tfrac12*(3^{11} + (-1)) = 88573 = 23*3851
621
(k + 1)! + (k + 1) (k + 1)! = (1 + k + 1) (k + 1)! = (k + 2) \left(k + 1\right)! = (k + 2)!
2,618
-E \cdot E + C^2 = (C - E) \cdot \left(E + C\right)
21,620
3500^2 \cdot 2 = 10^5 + 10^5 + 30^5
13,664
\frac{1}{2 \cdot x} = \frac{\frac12}{x} \cdot 1
-30,906
10 = 20\cdot 0 + 10
23,197
A^s A^t = A^{t + s}
7,787
\frac{1}{k^{\frac{1}{2}}} = \frac{2}{k^{\frac{1}{2}} + k^{\dfrac{1}{2}}} < \dfrac{2}{k^{1 / 2} + (k + (-1))^{1 / 2}}
310
\tfrac{1}{S^2}\cdot \left(-x + S\right) = -\frac{x}{S^2} + 1/S
22,100
\frac{15\cdot a^2}{2} = 8\cdot a \cdot a - \dfrac{a^2}{2}
19,360
50 = (y + 10) \cdot y = y \cdot y + 10 \cdot y = y^2 + 10 \cdot y
-23,875
2 \cdot 3 + 5 \cdot \frac{16}{8} = 2 \cdot 3 + 5 \cdot 2 = 6 + 5 \cdot 2 = 6 + 10 = 16
-29,520
\frac{1}{2!}4! = \tfrac{24}{2} = 12
9,303
y^3 - 4\cdot y + 4\cdot (-1) = (y + 3\cdot (-1))\cdot \left(y^2 + 3\cdot y + 5\right) = \left(y + 3\cdot \left(-1\right)\right)\cdot (y^2 - 8\cdot y + 5) = (y + 3\cdot (-1))\cdot (y + 4\cdot (-1))^2
2,281
22/35 = 11/14*\tfrac{1}{15}12
28,029
\mathbb{E}\left(d_G*d_x\right) = \mathbb{E}\left(d_x\right)*\mathbb{E}\left(d_G\right)
-2,644
\sqrt{10}\cdot \sqrt{9} + \sqrt{25}\cdot \sqrt{10} - \sqrt{10} = -\sqrt{10} + 3\cdot \sqrt{10} + 5\cdot \sqrt{10}
40,570
4 + 2\cdot 11 = 26
33,066
5 \left(-1\right) + 20 = 15
-20,632
9\cdot q/\left(9\cdot q\right)\cdot (-3/8) = ((-27)\cdot q)/(q\cdot 72)
24,588
\pi - 2 = 2\cdot (-1) + \pi
30,169
E \cdot M = M \cdot E
36,723
\frac{1}{2^3}\cdot 6! = \frac{1}{8}\cdot 720 = 90
9,690
f + g = xy \Rightarrow x = (g + f)/y
17,393
5^2 = y^2 + z^2 \implies y = \left(25 - z^2\right)^{1/2}
5,935
(y \cdot z)^3 = y^3 \cdot z \cdot z^2
6,872
(a + 2\cdot \left(-1\right))^2 + 4\cdot \left(-1\right) = -4\cdot a + a^2
-2,141
\frac{1}{3}*\pi + \pi*2/3 = \pi
2,534
h \cdot g^r/h = (\frac{g}{h} \cdot h)^r
-1,325
\frac{1}{(-9) \cdot \frac12} \cdot (1/7 \cdot (-5)) = -5/7 \cdot \left(-\frac29\right)
28,932
f_1*T + f_2*T*x = T*\left(f_1 + f_2*x\right)
-24,846
\int \frac{1}{x^6}\,\mathrm{d}x = \frac{1}{x^5 \cdot (-6 + 1)} + C = -\frac{1}{5x^5} + C
21,189
1 = \dfrac{2}{7} + \frac{8}{35} + \dfrac{1}{35}12 + 1/7
-6,383
\frac{1}{3 \cdot (5 + y) \cdot (y + 8 \cdot (-1))} \cdot 6 = 3/3 \cdot \dfrac{1}{(8 \cdot (-1) + y) \cdot (y + 5)} \cdot 2
4,242
(-b + d)*(d + b) = d * d - b * b
-587
(e^{23\cdot \pi\cdot i/12})^{16} = e^{16\cdot i\cdot \pi\cdot 23/12}
-11,085
\left(x + 2\right)^2 + b = \left(x + 2\right)*\left(x + 2\right) + b = x * x + 4*x + 4 + b
28,525
\binom{20 + 4 + \left(-1\right)}{4 + (-1)} = \binom{23}{3} = 1771
21,819
\frac12(0 + 2) = 1
17,440
e^{2\cdot x} = e^x \cdot e^x
19,169
(a + (-1)) \cdot (1 + a) = a^2 + (-1)
-13,419
3 + 4\times 2 = 3 + 8 = 11
-16,005
-8\cdot \tfrac{9}{10} + \frac{1}{10}\cdot 7 = -\frac{65}{10}