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math_formulas

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14,182
\frac{90\cdot 2}{1.5 \cdot 1.5} = 80
755
\|E \cdot z\|^2 - \|Z \cdot z\|^2 = ( E \cdot z, E \cdot z) - ( Z \cdot z, Z \cdot z) = ( E^2 \cdot z, z) - ( Z^2 \cdot z, z) = ( \left(E^2 - Z^2\right) \cdot z, z)
27,116
(h - f)^2/12 + \left((h + f)/2\right)^2 = \frac13(f^2 + h * h + fh)
-1,470
2*\dfrac{1}{7}/\left(\left(-4\right)*1/9\right) = -9/4*\dfrac{2}{7}
14,022
x^3 + 2 x^2 + x + 2 = (1 + x^2 + 0 x) (2 + x)
18,899
|g| - \ln\left(|b|\right) = -\ln(|b|) + |g|
22,565
e^y \cdot e^{y + 1} = e^{y + y + 1} = e^{2 \cdot y + 1}
-18,423
\dfrac{1}{(x + 10)*x}*(x + 10)*(x + 4*(-1)) = \frac{1}{x * x + 10*x}*(x * x + x*6 + 40*(-1))
4,323
1^3 + 2 \times 2 \times 2 + ... + l^3 = (1 + 2 + ... + l)^2
7,613
\mathbb{E}[X] \times \mathbb{E}[Y] = \mathbb{E}[Y \times X]
22,180
x + \left(-6x + 240\right)/12 = x/2 + 20
5,036
\frac 1{\cos^2 t }= 1 + \tan^2 t
33,455
1\cdot 3+3 \cdot 3+3\cdot6 = 30
19,132
0 \leq z + 3 \cdot (-1) \Rightarrow 3 \leq z
8,400
\tfrac{1}{2} - x/2 = (1 - x)/2
8,961
-D \cdot A + B \cdot A + B \cdot D = -A \cdot D + B \cdot A + B \cdot D
-3,807
\frac{18 t^5}{t\cdot 42} = \tfrac{t^5}{t}\cdot 18/42
-4,152
\frac{36}{66}\cdot \frac{q^5}{q^4} = \dfrac{36\cdot q^5}{66\cdot q^4}
25,082
r \cdot r\cdot A\cdot x = x\cdot r^2\cdot A
-20,849
\frac{1}{2 + x}(x + 2)\cdot 7/1 = \frac{1}{2 + x}(x\cdot 7 + 14)
36,888
5400 = \binom{5}{2}*3!*3*6*5
4,563
\frac{1}{\left(-a/y + 1\right)^2\cdot y \cdot y} = \frac{1}{(y - a)^2}
-14,128
6 + \dfrac{56}{7} = 6 + 8 = 6 + 8 = 14
2,954
x \cdot f = -(1 - x \cdot f) + 1
9,179
(f + a) \cdot (f + a) = a^2 + 2 \cdot a \cdot f + f^2
18,537
\frac{1}{3}*(d + 2) = 2 \Rightarrow d = 4
18,118
(x^2 + z * z)^2/2 + \frac12*(x^2 - z^2) * (x^2 - z^2) = x^4 + z^4 = (x^2 + z * z)^2 - 2*(x*z)^2
5,542
\cot(-\dfrac{1}{2}*37*\pi) = 0
3,645
D \cap Y = Y\Longrightarrow \left\{Y, D\right\}
12,576
\frac{1}{G X} = 1/(X G)
32,970
(0, ∞) = (0, 1)
22,989
y + \frac{p}{y} = q\Longrightarrow y = \left(q \pm \sqrt{-p*4 + q^2}\right)/2
19,099
x \cdot x^{l + (-1)} = x^l
8,153
\tan^2(z\times d) = \tan^2(-z\times d)
6,538
\left(-1\right) + k*2 = ((-1) + k*2) (2 + (-1))
-4,345
\dfrac{p^3}{p^2} = \dfrac{pp p}{pp} = p
29,676
z*y*y = y*z*y
-10,590
-\dfrac{1}{60 \cdot t} \cdot 4 = -\frac{1}{15 \cdot t} \cdot \frac{1}{4} \cdot 4
19,751
\frac{1}{\sqrt{2}}\cdot \pi = \tfrac{\pi\cdot \sqrt{2}}{2}
1,095
2a - a + 1 = 2a - a + \left(-1\right) = a + (-1)
16,212
991 + 109 \times (-1) + 840 \times 883 = 882 + 840 \times 883
-1,325
(\tfrac17*(-5))/(\frac12*(-9)) = -\frac57*\left(-\frac{2}{9}\right)
16,159
(3 + 6 + 9)/2 + \dfrac12 \cdot (3 + 9) = 9 + 6 = 15
18,920
(\frac12\cdot e)^n = (1/2)^n\cdot e^n
27,056
-o + 21 = 3\cdot 7 - o
38,714
\sum_{i=1}^{n + 1} a_i\cdot x_i = \sum_{i=1}^n a_i\cdot x_i + a_{n + 1}\cdot x_{n + 1} = (1 - a_{n + 1})\cdot \sum_{i=1}^n \frac{1}{1 - a_{n + 1}}\cdot a_i\cdot x_i + a_{n + 1}\cdot x_{n + 1}
28,026
\frac{1}{2 + (-1)} \cdot (2 \cdot (-1) + 10) = 8
49,490
8\cdot (-1) + 32 = 24
32,891
\sin{8\cdot x} = \sin{8\cdot \left(T + x\right)}\Longrightarrow 2\cdot \pi + 8\cdot x = (T + x)\cdot 8
-11,764
\frac{1}{100} = (10^{-1})^2
-9,846
-1^{-1} \cdot \tfrac{8}{25}/20 = \frac{1}{1 \cdot 25 \cdot 20} \cdot ((-1) \cdot 8) = -\frac{1}{500} \cdot 8 = -\frac{2}{125}
20,514
\binom{20}{7} = \frac{1}{7! \left(20 + 7(-1)\right)!}20! = 77520
-19,203
\frac{1}{3} = A_s/\left(81\cdot \pi\right)\cdot 81\cdot \pi = A_s
-9,598
0.01\cdot \left(-37\right) = -\dfrac{1}{100}\cdot 37.5 = -3/8
-11,627
i \cdot 21 + 3 = -9 + 12 + 21 i
5,409
r_i\cdot p_i + p_x\cdot r_j - p_x\cdot p_i\cdot r_j = \left(1 - p_i\right)\cdot r_j\cdot p_x + r_i\cdot p_i
-3,863
9/4\cdot z^3 = \frac{9}{4}\cdot z^3
568
g*f = (-g^2 + (f + g)^2 - f * f)/2
3,706
1 - \cos{x} = 2\cdot \sin^2{x/2} \leq \frac{1}{2}\cdot x^2
9,896
-a + a \cdot d \cdot a = \tfrac{1}{-\frac{1}{a} + \tfrac{1}{a - \frac{1}{d}}}
-4,565
(2 + x)\times \left(3 + x\right) = x^2 + x\times 5 + 6
-29,730
\frac{\mathrm{d}}{\mathrm{d}y} (3 + y^4 \cdot 4 - y^3 \cdot 7) = -y^2 \cdot 21 + 16 \cdot y^3
24,610
1 + 34/55 = \frac{1}{55} \cdot 89
17,414
\cos{\tfrac{1}{6} \cdot \pi} = \sqrt{3}/2
-457
\left(e^{i*\pi*5/4}\right)^6 = e^{6*\frac54*\pi*i}
38,837
\frac{3}{1 - \frac{1}{10}} = \frac{10}{3}
9,198
1/f = f^{\frac{a}{y}}\cdot f^{\frac1a\cdot y} = f^{a/y}\cdot f^y
6,247
\left( 3, 4, 2\right)^T - 2/3 ( 2, 6, 3)^T = ( 5/3, 0, 0)^T = \frac135 ( 1, 0, 0)^T
43,953
937\cdot 13 = 1 + 2436\cdot 5
2,681
\binom{(-1) + m}{0} = \binom{m}{0}
37,877
3\cdot 4 + 5\cdot 4 + 4\cdot 3 = 8\cdot 8 - 5\cdot 4
16,697
80 = 40 + 2 \cdot 10^2 - 16 \cdot 10
3,797
-x*(f + g) = -x*(g + f)
12,753
(q - (q + (q\cdot \ldots)^{1/2})^{1/2})^{1/2} = \left(\left(1 + 4\cdot (q + \left(-1\right))\right)^{1/2} + (-1)\right)/2
15,029
\frac{1}{4 + (y + (-1))^2} = \frac{1}{5 + y^2 - 2\cdot y}
25,373
\frac{1}{4}\cdot (1 + 1)\cdot \left(1 + 3\right)\cdot (1 + 2) = 6
21,241
\frac{12!}{4!*1!*1!*6!} = 27720
25,807
0 - 1/\left(2\cdot 6\right) = -1/12
3,279
1 + 2^0 + 2^1 \cdots*2^{n + (-1)} = 2^n
11,805
\dfrac{2\cdot \tan\left(z/2\right)}{1 + \tan^2\left(z/2\right)}\cdot 1 = \sin\left(z\right)
2,241
p - 1/2 = p - \tfrac{1}{2} \cdot (p + 1) = \dfrac{1}{2} \cdot (p + (-1))
25,513
(y + 1)^2 = y^2 + 2y + 1
28,214
3 \cdot \frac{1}{10}/2 = \frac{1}{20} \cdot 3
22,889
4\cdot y = 2\cdot 2\cdot y
-4,616
5*(-1) + x^2 - 4*x = (1 + x)*(x + 5*\left(-1\right))
19,958
1000 = 30 \cdot 30 + 10 \cdot 10
4,852
d/dx e^x = d/dx (x \cdot 4)
14,422
\frac{3}{3 + 5}*\left(1 - 0.4\right)*0.4*\frac{1}{8 + 4} 8 = 3/50
10,400
-x - x \times x = \frac{1}{1 - x}\times (x^3 - x) = \frac{1}{1 - x}
33,618
2^{b/2} = (\sqrt{2})^b
18,441
f*l + l*h = l*(f + h)
-6,732
20/100 + 2/100 = 2/10 + 2/100
39,359
5^{2k} = (5^2)^k = 25^k
6,122
\frac{1}{HA} = 1/(HA)
2,165
1/(T\cdot S) = \dfrac{1}{T\cdot S}
15,161
\frac{x^3-1}{x-1}=x^2+x+1
5,385
15/28 = 180/336
18,819
c_1 \cdot c_2 = \frac12 \cdot (c_2 + c_1)^2 - c_2^2/2 - \frac{c_1^2}{2}
15,687
1-\frac{6}{36}=\frac{30}{36}=\frac{5}{6}
24,181
b \cdot c \cdot c = c = b \cdot c \cdot c