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ddrg
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math_formulas

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20,806
h + g = ( h, g) \cdot ( 1, 1) \leq \left(h^2 + g^2\right)^{\frac{1}{2}}
11,708
\frac{11}{12}\cdot \pi = \pi\cdot 8/12 + 3\cdot \pi/12
1,357
(b^2 + a^2)^p = a^{2p} + ... + a^p b^p {p \choose \frac{p}{2}} + ... + b^{2p}
18,202
5*x^2/4 \leq 2 rightarrow x^2 \leq 8/5
47
(\tfrac{1}{4})^{3/2} = (\sqrt{1/4})^3 = \sqrt{1/64}
10,333
\dfrac{1}{b^2}\cdot b^3 = b
28,443
\left|{1/S}\right| \left|{S}\right| \left|{-E + \lambda x}\right| = \left|{x\lambda - E}\right| \left|{S}\right| \left|{1/S}\right|
32,731
\pi \cdot y \cdot \left(2 \cdot j + 1\right) = \pi \cdot N \Rightarrow \frac{1}{1 + j \cdot 2} \cdot N = y
30,062
8^{\frac{1}{2}}*2^{1 / 2} = 4
-8,451
(-9)\cdot 7 = -63
4,364
x^3 + (-1) = (x + (-1))\cdot \left(x^{3 + (-1)} + x^{3 + 2\cdot \left(-1\right)} + x^{3 + 3\cdot (-1)}\right) = (x + \left(-1\right))\cdot (x^2 + x + 1)
23,193
\left(-1\right) + 2\times \cos^2{z} = -\sin^2{z} + \cos^2{z}
43,189
20 \cdot 3 + 50 \cdot \left(-1\right) = 10
-7,225
\dfrac{3}{55} = \dfrac{3}{10}*\tfrac{2}{11}
17,004
3 = \sqrt{7950/30 - 16 \cdot 16}
-4,214
8/7\cdot z = z\cdot 8/7
5,572
(x_2 + x_1) \cdot (x_2 + x_1) = 2! \cdot x_1 \cdot x_2 + x_1^2 + x_2 \cdot x_2
36,361
|5403-5403|=0
24,252
(y + 1) (y + (-1)) = y^2 + (-1)
-11,446
{4} \cdot \left(6h + 4i \right)= {4} \cdot -9 \cdot \dfrac{ 5h - 10j }{ {4} } = -9 \cdot \left(5h - 10j \right)
11,685
\frac{1}{w^2 + 5} + 4 = \frac{1}{w^2 + 5}*(1 + 4*\left(w^2 + 5\right)) = \frac{4*w^2 + 21}{w^2 + 5}
-7,017
\dfrac{2}{7}*3/8/6 = \dfrac{1}{56}
-19,707
\frac{1}{7}\cdot 54 = \frac67\cdot 9
-2,401
(-5)^2 \cdot (-5) = \left(-5\right)\cdot (-5)\cdot (-5) = 25\cdot \left(-5\right) = -125
30,936
\tfrac{1}{6} = \frac{1}{2\cdot 3} = 0.1
43,333
2380*10 = 23800
877
z^2 + z \cdot 6 + 5 = \left(1 + z\right) \cdot (5 + z)
29,286
13832 = 20^3 + 18^3 = 24 * 24 * 24 + 2^3
14,422
(1 - 0.4) \cdot \frac{3}{5 + 3} \cdot 0.4 \cdot \frac{8}{4 + 8} = 3/50
23,496
\sin{t} \cdot \cos{y} - \cos{t} \cdot \sin{y} = \sin\left(-y + t\right)
10,340
c \cdot c \cdot c = c^3
14,446
\dfrac{3}{11} = \dfrac{3 \cdot 1}{4 \cdot 2 + 1 \cdot 3}
20,176
-f \cdot f = -f \cdot f
22,675
B \cap (F) = F \cap (B \cap F) = B \cap F
16,253
-x\cdot v = v\cdot (-x)
-19,121
\frac{59}{60} = G_q/\left(16\cdot \pi\right)\cdot 16\cdot \pi = G_q
-11,550
-i \cdot 24 + 8 = -8 + 16 - 24 \cdot i
-12,350
\sqrt{11}*2 = \sqrt{44}
-27,622
4\cdot (-1) + 21 = 17
-20,182
-\frac{36}{r \cdot 81 + 18 \cdot (-1)} = -\frac{4}{9 \cdot r + 2 \cdot \left(-1\right)} \cdot \frac{1}{9} \cdot 9
-22,962
\tfrac{135}{150} = 9\times 15/(15\times 10)
-1,507
\dfrac{4}{3} \div \dfrac{9}{5} = \dfrac{4}{3} \times \dfrac{5}{9}
38,869
\sqrt{2} \cdot 2 - 2 = 2 \cdot (-1 + \sqrt{2})
12,933
\frac{1}{1 + z} = (1 + i + z - i)^{-1} = \frac{1}{\left(1 + i\right) \cdot (1 + \frac{1}{1 + i} \cdot (z - i))}
2,964
\cos{z} \sin{x} + \cos{x} \sin{z} = \sin(x + z)
4,101
-y^3 + y^2 + 2\cdot (-1) = \left(2\cdot \left(-1\right) - y^2 + y\cdot 2\right)\cdot (1 + y)
36,937
3 - 2*x - z = 0 \implies z = -x*2 + 3
3,044
\frac{\binom{1}{1}\cdot \binom{10}{1}}{\binom{11}{2}} = 2/11
-24,721
\frac{l + 4}{16 (-1) + l^2} = \frac{1}{16 (-1) + l^2}(2l + 2(-1)) + \frac{6 - l}{16 (-1) + l * l}
41,531
|X| = |X| \times |X| = |X \times X|
-1,902
\pi \cdot 17/12 = \dfrac14 \cdot 5 \cdot \pi + \pi/6
44,085
6344 = 2^3 + 8^3 + 12^3 + 16^2 \cdot 16
-3,984
\frac{p^4 \cdot 90}{p \cdot 81} = p^4/p \cdot \frac{90}{81}
10,882
x \cdot (e + b \cdot 0) = x \cdot e + 0 \cdot b
-12,837
8 = 11\cdot \left(-1\right) + 19
-1,810
\frac{\pi}{6} - \dfrac{\pi}{6} = 0
15,410
x^2 + (-1) = \left(1 + x\right)\cdot (\left(-1\right) + x)
12,370
(x + 2y)^2 = 4(xy)^2 - 24 xy + 49 = 4xy*(xy + 6(-1)) + 49
4,895
\frac{y^2 + \left(-1\right)}{(-1) + y} = y + 1
-7,063
6/15*5/14 = \dfrac{1}{7}
-30,022
n \cdot z^{\left(-1\right) + n} = \frac{\mathrm{d}}{\mathrm{d}z} z^n
3,618
\left(1 + x\right)^2\times 2 = x \times x\times 2 + x\times 4 + 2
36,612
f_2 f_1 = f_2 f_1
-6,297
\frac{3}{3x + 27 \left(-1\right)} = \frac{1}{(x + 9\left(-1\right)) \cdot 3}3
33,336
\frac{41 s + 420}{20 (-1) + s^2 - s} = -\dfrac{256}{9(s + 4)} + \dfrac{1}{9(s + 5(-1))}625
11,213
y + 6 = (x^2 + y^2)^{1/2} \Rightarrow 36 + y \cdot 12 = x^2
11,807
a^2 + b \cdot b + a^2\cdot b \cdot b = (a - b)^2 + 2\cdot a\cdot b + a^2\cdot b^2 = 1 + 2\cdot a\cdot b + a^2\cdot b \cdot b = \left(1 + a\cdot b\right)^2
14,540
\frac{1}{g \times \frac{1}{f}} = f/g
38,306
\tau^2 = \tau^2
11,993
x * x + d * d + 2*d*x = (d + x)^2
6,530
b^j f = f b^j
6,710
\frac{d\eta}{dt} = -x\sqrt{\frac{1}{\eta}} \eta = -x\sqrt{\eta}
7,909
|I - A B| = |-A B + I|
20,026
\frac{A\cdot B}{A}\cdot 1 = \frac{C}{A} \Rightarrow \frac{C}{A} = B
31,840
\chi\cdot \frac{1}{\chi\cdot n}\cdot n = \frac1n\cdot n
1,518
1 + d^2 \cdot d = (1 + d)\cdot (1 - d + d \cdot d) = (1 + d)\cdot \sqrt{3}\cdot d
26,264
10^2*2 + 2*10^1 + 10^0*9 = 229
13,764
z^{2^n} = \left(z^4\right)^{2^{n + 2\cdot (-1)}} = (z + 1)^{2^{n + 2\cdot (-1)}} = z^{2^{n + 2\cdot (-1)}} + 1
6,366
(l - x)! = (1 + l - 1 + x)!
7,096
(3 + y)\cdot (y + 1) = y \cdot y + 4\cdot y + 3
1,998
\frac{58!}{38!} = 3*13*\frac{58!}{39!}
31,646
(x + a + h) (a \cdot a + h^2 + x^2 - ah - hx - xa) = a^3 + h \cdot h^2 + x^3 - 3xh a
-710
(e^{23 \cdot \pi \cdot i/12})^{13} = e^{\frac{23}{12} \cdot \pi \cdot i \cdot 13}
12,152
(y + \left(-1\right))^2 + 1 = -2\cdot y + y^2 + 2
9,221
-6\cdot x - 24 = -(12 + x\cdot 3)\cdot 2
-5,449
\frac{1}{1000} 16.8 = \frac{1}{1000} 16.8
41,297
419^3 - 362 * 362 * 362 = 26122131 = 235^3 + 236 * 236 * 236 = 107^3 + 292 * 292 * 292
-9,494
-x \cdot x \cdot 7 \cdot x + x \cdot x \cdot 5 \cdot 7 = -7 \cdot x^3 + 35 \cdot x^2
4,803
c^2 + b^2 = -2*b*c + (b + c)^2
53,184
x^2 = x^2 + 1 + \left(-1\right) = x^2 + 1 + 1 = x^2 + 1^2 + 1^2 = x + 1 + x + x + 1 = x + x + x + 1 + 1 = x
38,081
\left(2 = \frac{2}{z^2} + 1 - \dfrac{4}{3\times z} \implies z \times z\times 6 = z \times z\times 3 - 4\times z + 6\right) \implies 3\times z \times z + 4\times z + 6\times (-1) = 0
16,134
600 + 420 + 91 = 16 \cdot 16 + 11^2 + 12^2 + 13^2 + 14^2 + 15^2
-4,448
\left(z + 2\cdot (-1)\right)\cdot \left(3 + z\right) = z^2 + z + 6\cdot (-1)
13,643
(2\cdot (5\cdot r + 4))^2 + 2\cdot (5\cdot r + 4) = 100\cdot r^2 + 160\cdot r + 64 + 10\cdot r + 8 = 10\cdot (10\cdot r^2 + 17\cdot r + 70) + 2
11,310
z^2 = (z + (-1)) (1 + z) + 1
14,507
(-8)^{\frac13 \cdot 4} = -(-1)^{\dfrac{1}{3}} \cdot 16
-7,160
15/49 = \frac{3}{7}\cdot 5/7
-4,092
\tfrac{1}{16} \cdot 4 \cdot \tfrac{t^4}{t^5} = \frac{4 \cdot t^4}{t^5 \cdot 16}
7,922
\frac{g \cdot 1/d}{g \cdot 1/d} = 1 = d g/d/g
20,022
(z + y)^2 = z^2 + zy + zy + y^2 \gt z^{2 - y} + y^{2 - z}