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ddrg
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math_formulas

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int64
-30,985
55.9k
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25,344
\binom{(-1) + 17}{3} + \binom{17 + (-1)}{2} + \binom{(-1) + 17}{2} = 800
-20,357
\dfrac{(-14)\cdot y}{28\cdot y + 63\cdot (-1)} = 7/7\cdot \frac{y\cdot (-2)}{y\cdot 4 + 9\cdot (-1)}
6,584
(y^2 - c\cdot y + (-1))\cdot (y \cdot y + c\cdot y + (-1)) = (y^2 + (-1))^2 - c \cdot c\cdot y^2 = y^4 - (2 + c^2)\cdot y^2 + 1
-11,098
(z + 4)^2 + d = (z + 4) \cdot (z + 4) + d = z^2 + 8 \cdot z + 16 + d
-647
e^{2 π i} = \left(e^{π i}\right)^2 = (-1)^2 = 1
25,967
2*b + 3*b = 10\Longrightarrow b = 2
9,767
l + 2\cdot (5\cdot z + 3) = 10\cdot z + 6 + l
16,393
-\dfrac{1}{c + x}c + 1 = \frac{1}{c + x}x
13,346
-2*p*x*D_1^2*D_2 * D_2 + 2*p*(D_1*D_2)^2*x = p*(-D_2*D_1 + D_1*D_2)^2*x
-20,626
(8\cdot y + 9)/\left(5\cdot y\right)\cdot 3/3 = \frac{1}{15\cdot y}\cdot \left(24\cdot y + 27\right)
1,197
3 \cdot 2^{n + 1} = 3 \cdot 2^n + 3 \cdot 2^n \gt 4 \cdot n \cdot n + 1 + 4 \cdot n^2 + 1
2,979
(-3*\sqrt{y^2 + (-1)} + 4)/(y*5) = \sin{r} \Rightarrow 9*\left(y * y + (-1)\right) = (4 - 5*\sin{r}*y)^2
4,896
q \cdot q/4 - \frac{2}{16} = \frac14 \cdot q \cdot q - 1/8
-10,362
-\frac{1}{3\cdot n}\cdot 6\cdot 12/12 = -72/(n\cdot 36)
6,934
q^{(-1) + f}\cdot q = q^f
32,558
12 = \left(1 + 1 + 2\right)*3
23,197
A^{r + p} = A^r*A^p
18,978
(l + 5)^3 = l^3 + l^2 \cdot 15 + 75 \cdot l + 125
3,547
-y^3 + x^3 = (x^2 + x*y + y^2)*\left(-y + x\right)
29,851
\dfrac{1}{216}\cdot 181 = 1 - \tfrac{1}{216}\cdot (5 + 5 + 8 + 9 + 8)
6,543
2014 + 21*(-1) = 1993
21,777
z*(m + 1)*4 = (m*4 + 4)*z
-9,124
q \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 = 72 \cdot q
36,969
(gf' + fg') h + fg h' = fgh' + f' gh + hg' f
31,308
Y^{l + n} = Y^n Y^l
24,645
\sqrt{x}/x = \frac{\sqrt{x}}{\sqrt{x}\cdot \sqrt{x}} = 1/(\sqrt{x})
17,007
1 = \tfrac133 = 3*0.333 \dotsm = 0.999 \dotsm
20,664
\cosh^2(x) = \frac{(e^{x}+e^{-x})^2}{4} = \frac{e^{2x}+e^{-2x}+2e^0}{4}
894
\frac{4321}{4322}*4322/4323/4321 = \frac{1}{4323}
-29,061
c^6*c^0 = c^6
23,829
\dfrac{1}{3 + (-1)}\cdot 2 = 1
43,510
0 = 0\times 1^{-1}/1
-2,359
(-10)^3 = (-10) \times \left(-10\right) \times (-10) = 100 \times (-10) = -1000
34,443
-4*a * a + b^2 = (a*2 + b)*(b - 2*a)
12,565
t^{\dfrac{5}{2}} = \dfrac{1}{t^{1/2}}\cdot t^3
28,802
(1 + n)\cdot n! = (n + 1)!
-20,417
4/4*\frac{(-6)*t}{t + 3} = \dfrac{1}{4*t + 12}*(t*(-24))
7,868
e z/e = z
11,239
(d^\beta)^l = d^{\beta\cdot l} = d^{l\cdot \beta}
21,582
(H_2^2 - H_1 \cdot H_2 + H_1^2) \cdot (H_2 + H_1) = H_1^3 + H_2^3
5,848
1/\left(a*c\right) = 1/(a*c)
28,207
\frac{n!}{(n - r)!*r!} = \binom{n}{r}
-20,360
\frac{10}{10} \cdot \tfrac{1}{k + 9} \cdot (4 + k \cdot 4) = \frac{40 + 40 \cdot k}{10 \cdot k + 90}
7,775
4\cdot k^2 = -\left(k^2 + (-1)\right)^2 + (1 + k^2) \cdot (1 + k^2)
35,754
x^2 - 2\cdot i = x \cdot x - (1 + i)^2 = (x + (-1) - i)\cdot (x + 1 + i)
34,896
\left(-1\right) + \dfrac{100}{4} = 24
-9,257
10 + 50*t = t*2*5*5 + 2*5
6,227
\sec(x) := \frac{1}{\cos\left(x\right)}
17,004
3 = \left(-16^2 + \frac{7950}{30}\right)^{1 / 2}
-7,630
(10 - 5 \cdot i - 20 \cdot i + 10 \cdot \left(-1\right))/5 = \tfrac{1}{5} \cdot (0 - 25 \cdot i) = -5 \cdot i
-4,931
29.4*10^5 = 10^{5 + 0}*29.4
21,627
0 + (1 + x^2 + x) = x^2 + x + 1
-13,139
30.87\cdot \frac{1}{9}/(-0.7) = 30.87/(9\cdot \left(-0.7\right)) = \frac{1}{-6.3}\cdot 30.87
41,944
50 = 5a^1 + 0a^0 = 5a
27,927
2 = (5 + \sqrt{23})*\left(-\sqrt{23} + 5\right)
25,392
(2*n + 2)*(2*n + 1)*(2*n)! = (2*n + 2)!
50,000
8 + 10^6 = 1000008
19,416
\sqrt{\lambda^2} = \sqrt{(-\lambda)^2} = -\lambda
27,765
90 = z\cdot 8 rightarrow z = 45/4 = 11.25
19,849
2^{2 \cdot n} = \frac{1}{2} \cdot 2^{2 \cdot n + 1}
-3,920
11\times k = 11\times k
-3,440
\sqrt{11}\cdot (3 + 2) = 5\cdot \sqrt{11}
-17,502
84 = 18 + 66
-27,625
-3 + 5*(-1) + 2*\left(-1\right) = -8 + 2*(-1) = -10
29,189
\sqrt{z^6} = |z \cdot z \cdot z| = -z^3
12,619
-\frac{x}{d} = \tfrac{1}{d}\cdot (\left(-1\right)\cdot x) = x/((-1)\cdot d)
-16,581
9\sqrt{16} \sqrt{3} = 9 \cdot 4 \sqrt{3} = 36 \sqrt{3}
-20,261
9/9\cdot \frac{6\cdot (-1) + x\cdot 10}{8\cdot (-1) - x\cdot 3} = \frac{1}{-x\cdot 27 + 72\cdot \left(-1\right)}\cdot (54\cdot (-1) + x\cdot 90)
-16,503
\sqrt{32} \times 9 = 9 \times \sqrt{16 \times 2}
2,114
3x^3 + 10 x * x + 14 x + 8 = 3x^3 + 6x^2 + 6x + 4x^2 + 8x + 8 = (3x + 4) (x^2 + 2x + 2)
564
\alpha a = a \alpha
51,100
\frac{\partial}{\partial y} (y\cdot e^{-k\cdot y}) = y\cdot \frac{\partial}{\partial y} e^{-k\cdot y} + \frac{\text{d}y}{\text{d}y}\cdot e^{-k\cdot y} = -k\cdot y\cdot e^{-k\cdot y} + e^{-k\cdot y}
-5,248
18.8\times 10^{-4 + 5} = 18.8\times 10^1
-7,679
\frac{1}{-i + 4}(5i - 20) \frac{1}{i + 4}(i + 4) = \tfrac{1}{4 - i}(-20 + 5i)
26,380
2*(-1) + \frac{13^2}{5^2} = \dfrac{1}{5^2}*(12^2 - 5^2)
5,777
(2-\sqrt{3})(2+\sqrt{3})=1
30,036
p = \dfrac{1}{d^2} g^2 \implies d^2 p = g^2
6,978
(-(f - g) \cdot (f - g) + (g + f)^2)/4 = g\cdot f
18,185
Y/X = G/D = \frac{Y + G}{X + D}
251
\frac{26}{27} \cdot 3/51 + \frac{1}{27} = \frac{1}{459} 43
18,275
\tfrac{1}{\frac{1}{x + x} + \frac{1}{x + x}} = x
30,112
2 \cdot \sin(\pi/18) = 2 \cdot \cos\left(4 \cdot \pi/9\right)
870
(4^2 + 3^2)\cdot 5^2 = 5^4
10,719
(-z + 1)\cdot (1 + z) = 1 - z^2
37,805
\sqrt{z} = z^{\dfrac12}
-20,347
8/8*\frac{1}{-10}*(-n*5 + 2*(-1)) = \dfrac{1}{-80}*(16*(-1) - n*40)
12,964
\cos(a + b) = \sin(\pi/2 - a - b) = \cos(a) \cos(b) - \sin(a) \sin(b)
4,808
(-\beta + x) \cdot \left(x + \beta\right) = x \cdot x - \beta^2
2,936
(-x^2 + b^2)/2 = -\frac{1}{2} \cdot x^2 + \frac12 \cdot b \cdot b
2,943
e^{\frac{1}{\dfrac1x}} = e^x
14,466
\dfrac{0*\left(-1\right) + f}{f - a} = \frac{f}{-a + f}
-11,980
\dfrac{7}{24} = \dfrac{s}{16\pi} \times 16\pi = s
-5,316
38.4 \times 10^{-2\,+\,4} = 38.4 \times 10^{2}
24,690
1/6 + 1/6 = \dfrac{1}{3}
-3,286
2^{1 / 2}*\left(5 + 3\left(-1\right)\right) = 2*2^{1 / 2}
12,464
((-1)*0.5 + m)^2 = m^2 - m + 0.25
34,054
( 1, -1/3) = \left[-1, 5\right] = [1, 2]
-15,382
\dfrac{t^3}{i\times t^2}\times \frac{1}{i^6} = \dfrac{(\dfrac{t}{i \times i})^3}{i\times t \times t}
33,027
100 \left(-1\right) + 200 = 100
-23,551
\frac{1/8}{2} \cdot 3 = 3/16