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math_formulas

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-260
\frac{8!}{(8 + 6(-1))!*6!} = \binom{8}{6}
-3,865
\tfrac{\dfrac{1}{2}*3}{x * x * x} = \frac{3}{2*x^3}
-28,641
6 \cdot x \cdot x + 36 \cdot x + 78 = 6 \cdot (x \cdot x + 6 \cdot x + 13) = 6 \cdot (x \cdot x + 6 \cdot x + 9 + 4) = 6 \cdot ((x + 3)^2 + 4) = 6 \cdot ((x + 3)^2 + 2^2)
15,739
-3 \cdot \left(2^{20} + (-1)\right) + 3^{20} = 3 \cdot (1 + 3^{19} - 2^{20})
26,745
\left(2*k\right)^2 = 2*(m*2)^2 \implies k * k = 2*m^2
29,722
f*y*z = y*z = y*z = f*y*z
8,348
(a + 1) (d + 1) + (-1) = a + d + ad
5,170
\frac{a^3 - b^3}{a^2 + a \cdot b + b^2} = -b + a
6,275
1/30 = \frac{1}{3}\cdot \frac{1}{10}
-19,623
1/(5/9\times 6) = 9\times 1/5/6
42,416
\frac{1}{30} \cdot 10 = 1/3
-5,617
\frac{5}{4\times \left(8 + t\right)} = \frac{5}{32 + t\times 4}
8,689
1 + y^{1/3} = 0 rightarrow y^{1/3} = -1
29,070
C_2*B*C_1 = B*C_1*C_2
3,635
y^2 - 4 \times y + 12 \times (-1) = (y + 6 \times (-1)) \times (2 + y)
38,279
56 = 2 2*14
42,509
2 2 \cdot 0.01 + 0.02 = 0.06
-10,450
-4 = -5 + j + 1 = j + 4\cdot \left(-1\right)
4,936
(-1) + \mathbb{E}[T] = \mathbb{E}[(-1) + T]
14,106
80 = \tfrac13\cdot 2\cdot 120
5,851
e^{(\left(-1\right) \cdot x)/2} \cdot e^{\frac12 \cdot \left(x \cdot \left(-1\right)\right)} = e^{-x}
2,820
m\cdot 8 = m\cdot (3 + 5)
33,222
(-f + h)^2 = f^2 + h^2 - 2\cdot h\cdot f
-27,661
\tfrac12 7 = \dfrac{7}{2}
11,427
V \cdot Y + V \cdot W = V \cdot (W + Y)
8,301
0 = z^3 - 2z^2 - 5z + 6 = (z + (-1)) (z + 2) \left(z + 3\left(-1\right)\right)
-11,912
0.01601 = 1.601 \cdot 0.01
30,947
6^x = (3 \cdot 2)^x = 3^x \cdot 2^x = 2^x + 2^x \cdots \cdots
6,227
\sec(\theta) := \frac{1}{\cos\left(\theta\right)}
17,188
n + 2(-1) = n + 4(-1) + 2
33,872
1 + x \cdot x + \left(-1\right) = x^2
7,991
p = -\dfrac{1}{2 \cdot q} \cdot \left(\left(-2\right) \cdot q \cdot p\right) = -\frac{1}{2 \cdot q} \cdot ((-1) \cdot q \cdot p^2)
-19,587
\dfrac{7*\frac{1}{4}}{1/5*9} = 5/9*\dfrac{7}{4}
24,314
\left(-b + x\right) \left(x + b\right) = x x - b^2
18,431
\left(6\cdot l_1 + 3\cdot (2\cdot l_2 + 1) = 9 = 6\cdot \left(l_1 + l_2\right) + 3 \implies 1 = l_1 + l_2\right) \implies 1 - l_2 = l_1
-23,246
2/9 = \frac42\frac{1}{9}
30,636
36 = 3! \cdot 2! \cdot 3
6,866
\dfrac{x^2 + x}{(-1) \cdot x} = (-1) - x
8,146
\frac{1}{(1 - w \cdot w) \cdot (1 - w \cdot w)} = \frac{1}{((w + (-1)) (w + 1)) \cdot ((w + (-1)) (w + 1))} = \frac{1}{(w + (-1))^2 (w + 1) \cdot (w + 1)}
75
1/33 + \frac{1}{11} + \frac{1}{22} = 1/6
19,756
0\cdot ( 1, 4, 0) + ( 2, 2, 2)\cdot 0 = 0
-1,860
\pi\cdot \frac{11}{6} - \frac16\cdot \pi = \pi\cdot 5/3
-22,290
21 + y^2 - y\cdot 10 = (y + 3\cdot \left(-1\right))\cdot (y + 7\cdot (-1))
-20,030
\frac{1}{5x + 2}\left(x \cdot 5 + 2\right) \tfrac{1}{7}4 = \frac{1}{14 + 35 x}\left(8 + x \cdot 20\right)
12,553
E\left[N\right] E\left[X\right] = E\left[NX\right]
-14,125
\frac{1}{10 + 9(-1)}2 = \frac112 = \frac{2}{1} = 2
-20,407
\frac{1}{4} \cdot 4 \cdot \frac{3 - p \cdot 10}{(-1) \cdot 6 \cdot p} = \frac{12 - p \cdot 40}{(-24) \cdot p}
22,829
8/2 = \tfrac{1}{2}*2 + \frac{6}{2}
11,106
5! \cdot {26 \choose 3} \cdot {10 \choose 2} = 14040000
13,650
a^2 + b^2 = \dotsm = a \times a\times b \times b
-6,139
\frac{3 \cdot a}{12 \cdot (-1) + a^2 + a} = \dfrac{a \cdot 3}{(4 + a) \cdot (3 \cdot (-1) + a)}
4,013
b*h + h + b + 1 = (b + 1)*(1 + h)
27,118
\frac{\mathrm{d}z}{\mathrm{d}x} = \frac{1}{z^2} + 4\cdot (-1) = \frac{1}{z^2}\cdot (1 - 4\cdot z^2)
25,511
(36 + 1)^{1 / 2} = 6*(1 + \frac{1}{36})^{\frac{1}{2}} = 1 + 1/72 - \dots
-534
({ e^{23\pi i / 12}}) ^ {2} = e ^ {2 \cdot (23\pi i / 12)}
34,026
(R + 1)! = R!\cdot (R + 1)
-6,388
\frac{20}{4 \cdot (4 \cdot (-1) + q) \cdot (q + 6)} = 4/4 \cdot \frac{5}{\left(q + 6\right) \cdot \left(4 \cdot (-1) + q\right)}
-22,440
16^{-\dfrac{5}{4}} = (\frac{1}{16})^{\frac{1}{4}\cdot 5} = (\left(\frac{1}{16}\right)^{\frac{1}{4}})^5
-30,266
(y + 3)\cdot (y + 2\cdot (-1)) = 6\cdot (-1) + y^2 + y
28,070
25/36 = 2*5/6*5/6/2
38,495
x * y = y * x
49,105
495 = 5\times 9\times 11
22,305
q \cdot 6 = 0 rightarrow q = 0
23,790
1/3\cdot 4 = 4/3
15,155
\frac13*2 = \dfrac{2}{2 + 3 + 2*(-1)}
21,556
1/2 + ((-1) + m)/4 = (1 + m)/4
-6,667
\frac{5}{x*3 + 12 (-1)} = \frac{5}{(x + 4(-1))*3}
941
exp(y + B) = exp(B)\cdot exp(y)
3,125
\cos{\frac{1}{6} \cdot \pi \cdot 7} = \cos{\frac16 \cdot ((-1) \cdot 7 \cdot \pi)}
-3,536
\frac{1}{100} \cdot 35 = \frac{7 \cdot 5}{5 \cdot 20}
12,648
(n - k)!\cdot \binom{n}{k} = n!/k!
30,970
x = 2x/4\cdot 2
9,094
\left(A + y\cdot I\right)\cdot (x\cdot I + A) = (I\cdot y + A)\cdot (x\cdot I + A)
-18,571
3 \cdot z + 2 \cdot (-1) = 9 \cdot \left(2 \cdot z + 1\right) = 18 \cdot z + 9
32,128
S\cdot \beta = \beta\cdot S
24,320
E_s + E_s = E_s*2
568
fg = (-g^2 + (g + f)^2 - f^2)/2
18,803
1 = 1^{-1}*\frac{1}{1}/1
36,361
|5403 + 5403 \times \left(-1\right)| = 0
30,542
(5^{\frac{1}{2}})^2 - 2*5^{\frac{1}{2}} + 1 = (5^{1 / 2} + \left(-1\right))^2
30,107
32 + y^{15} \cdot 31 - y^{10} = 0 \implies 0 = \left(y^{15} + 1\right) \cdot 31 - \left(-1\right) + y^{10}
-11,564
-7i - 6 + 3\left(-1\right) = -9 - 7i
5,511
h' \times k' \times f \times l = f \times l \times k' \times h'
6,980
\frac{1}{d^{\frac12} g^{-3/2}} = \frac{g^{3/2}}{d^{\frac12}}
-3,927
110/10 \dfrac{m^5}{m^4} = \frac{110 m^5}{10 m^4}
25,434
-\frac{x}{2} + \frac{3}{x} = -x/2 + \frac3x
11,596
5^5 - 4 \cdot 5^4 + 6 \cdot 5^3 - 5 \cdot 5 \cdot 4 + 5 = 1280
5,576
3/6\cdot 4/10\cdot \frac23 = \frac{1}{15}\cdot 2
-5,394
10^6*59.4 = 10^{1 + 5}*59.4
22,570
f = b\Longrightarrow \left\{f,b\right\}
-26,502
9 + 25 x^2 - 30 x = 3^2 + (x\cdot 5)^2 - x\cdot 5\cdot 3\cdot 2
36,277
x^2 + 2 \cdot x \cdot y + y^2 = (x + y) \cdot (x + y)
20,858
X\frac{\mathrm{d}Y}{\mathrm{d}X} + Y = \frac{\partial}{\partial X} \left(YX\right)
28,365
(d - f) \cdot (d - f) = (d - f) \cdot \left(d - f\right) = d^2 - 2 \cdot d \cdot f + f^2
18,135
(z^2 + z\cdot 20 + 180)\cdot (18\cdot (-1) + z^2 - z\cdot 2) = z^4 + 18\cdot z^3 + z^2\cdot 122 - 720\cdot z + 3240\cdot (-1)
-2,245
-\frac{1}{11} + 5/11 = \dfrac{4}{11}
12,847
\frac{\frac{1}{6}}{6}*5/6 = \dfrac{5}{216} = 0.023
43,865
9 = 12 + 3 \cdot (-1)
6,140
1.73205081\cdot \dotsm/3 = \sqrt{3}/3
9,619
\sin\left(x + z\right) = \sin(x)*\cos\left(z\right) + \sin(z)*\cos(x) = \sin(x) + \sin\left(z\right)