ddrg/math_formulas · Datasets at Hugging Face

id int64 -30,985 55.9k	text stringlengths 5 437k
-20,981	\frac{1}{10 + p} \cdot 1 = \frac{1}{p \cdot 10 + 100} \cdot 10
32,948	\sin^6{z} = (\sin^2{z})^3 = (1 - \cos^2{z}) * (1 - \cos^2{z}) * (1 - \cos^2{z})
24,435	25^x = (1 + 24)^x
10,498	2 + z = \frac{1}{z + 2(-1)}(z^2 + 4(-1))
-9,192	-2 \cdot 2 \cdot 3 - q \cdot 2 \cdot 2 \cdot 2 \cdot 3 = 12 \cdot (-1) - 24 \cdot q
5,607	\frac{\partial}{\partial x} u^n = u^{\left(-1\right) + n}\frac{\mathrm{d}u}{\mathrm{d}x}n
42,282	1.2 = 0.3 \cdot 4
-5,732	\frac{4}{5 \cdot (-1) + 5 \cdot q} = \frac{4}{((-1) + q) \cdot 5}
22,967	2n - (-1) + n = n + 1
28,633	I = \frac{I^2}{I}
31,225	2520 = 3 \cdot 3\cdot 2^3\cdot 5\cdot 7
11,569	a \cdot x = \dfrac{1}{1/a \cdot 1/x} = \frac{1}{\frac1x \cdot \frac{1}{a}} = x \cdot a
-11,879	3.276*0.1 = 3.276/10
1,779	a^{\frac32} = a^{\frac{1}{2}} (a^{\frac12})^2
-4,520	y^2 - 6y + 5 = ((-1) + y)(y + 5*(-1))
1,655	\lambda\pi = \pin \Rightarrow \lambda = n
44,351	\frac{π}{1} = π
12,994	A_1 = 1\Longrightarrow \mathbb{E}[A_1] = 1
45,287	\frac25 = \dfrac15*2
25,254	{n + (-1) \choose (-1) + k}*\frac{n}{k} = {n \choose k}
-1,585	2\cdot \pi - \frac{1}{12}\cdot \pi = 23/12\cdot \pi
9,502	(-3/2 + 2)^2 = (-\frac12 \cdot 3 + 1)^2
19,290	\sqrt{2}/2 + \frac{\sqrt{2}}{2} \cdot i + \frac{\sqrt{2}}{2} - \sqrt{2} \cdot i/2 = \sqrt{2}
11,000	\frac{1}{A - B} = \frac{1}{(1 - \frac{B}{A}) \cdot A}
33,112	\frac{1}{2}\cdot (\left(-1\right) + 11) = 5
19,478	x + 2 = \frac12 \cdot (x \cdot 2 + 4 \cdot (-1)) + 4
10,254	(y + z) * (y + z) = y^2 + z^2 + 2zy
32,440	3\cdot \left(-1\right) + 2\cdot n = 2\cdot \left((-1) + n\right) + 3\cdot (-1) + 2
-9,632	0.01\cdot (-10) = -\dfrac{10}{100} = -\frac{1}{10}
5,110	4 \dfrac12 \left(p + 3\right) \frac12 (7 (-1) + p) = (3 + p) \left(7 \left(-1\right) + p\right)
-26,636	16 \cdot x^2 - y^2 \cdot 49 = (4 \cdot x + 7 \cdot y) \cdot (4 \cdot x - y \cdot 7)
-3,536	35/100 = \frac{1}{20\cdot 5}\cdot 35
387	57 \times 6 + 1 = 343 = 7^3
10,329	(1 + n)^3 = 1 + n^3 + 3 \cdot n \cdot n + 3 \cdot n
17,419	r \cdot r + r\cdot (-r + a) + \left(b - r\right)\cdot r = (a + b - r)\cdot r
-20,913	\dfrac99\cdot \frac{1}{2\cdot x + 8\cdot (-1)}\cdot (x\cdot (-4)) = \dfrac{1}{72\cdot (-1) + 18\cdot x}\cdot (x\cdot (-36))
-20,032	\frac{1}{5\cdot \left(-1\right) + r\cdot 10}\cdot (5\cdot (-1) + r\cdot 10)\cdot \frac{1}{7}\cdot 10 = \frac{100\cdot r + 50\cdot (-1)}{r\cdot 70 + 35\cdot (-1)}
-26,500	81 \cdot x^2 + 180 \cdot x + 100 = (x \cdot 9)^2 + 2 \cdot 9 \cdot x \cdot 10 + 10^2
12,979	(-1) + p + x = 1 + x + (-1) + p + (-1)
-20,485	\frac{5 + n}{9 - n} \dfrac55 = \tfrac{1}{-n \cdot 5 + 45} (25 + n \cdot 5)
-20,061	-\frac11 \cdot 3 \cdot \tfrac{\left(-8\right) \cdot p}{p \cdot (-8)} = \frac{24 \cdot p}{(-8) \cdot p}
-3,394	-\sqrt{16}\cdot \sqrt{6} + \sqrt{25}\cdot \sqrt{6} = \sqrt{6}\cdot 5 - 4\cdot \sqrt{6}
6,736	(ha + 1) \cdot (ha + 1) = a^2 h^2 + 2ha + 1
19,936	\frac{14}{7} = \frac77 \cdot 2
30,446	e^{6\eta} \eta = 1 \Rightarrow \eta \approx 0.2387
24,727	\frac{1}{3}\cdot 2 = \frac12 + \dfrac13 - \dfrac{1}{6}
-28,922	7/(7\cdot \frac{1}{20}) = 7\cdot \frac{20}{7} = 20
1,638	(x^3 \cdot x^9)^2 = x^{24}
28,870	A\cdot D = D\cdot B \implies 2\cdot A\cdot D = A\cdot B
-4,182	\frac{1}{x \cdot 24} \cdot x^5 \cdot 48 = \frac{x^5}{x} \cdot \frac{1}{24} \cdot 48
-428	-\pi \cdot 8 + \frac{115}{12} \cdot \pi = 19/12 \cdot \pi
20,208	2\cdot π - \frac{9}{5} - π\cdot 2 - \frac15\cdot 8 = -\dfrac{1}{5}
10,233	b^3 = 2 + 11\cdot i + 2 - 11\cdot i + 3\cdot \left((2 + 11\cdot i)\cdot (2 - 11\cdot i)\right)^{\dfrac{1}{3}}\cdot b = 4 + 15\cdot b
1,404	5(y + 9) (y + 2(-1)) (3(-1) + y) = y \cdot y \cdot y\cdot 5 + y^2\cdot 20 - y\cdot 195 + 270
34,763	1^2 + 40 \cdot 40 = 42^2 + 163 (-1)
-29,573	\tfrac{z^45}{z}1 = 5*z^3
-15,594	\frac{(m^5)^3}{(m^5\cdot y^3) \cdot (m^5\cdot y^3) \cdot (m^5\cdot y^3)} = \frac{m^{15}}{m^{15}\cdot y^9}
9,781	\frac14 = \cos(2 \cdot 0)/4
36,958	2^{x + 1} = 2.2^x \gt x \cdot x + x \cdot x
30,405	7^{62} = 7^{64}/49 = 1/49 = 1/49
7,254	\frac{1}{11 + 17}17 \cdot 84 = 51
16,312	2^{\sqrt{l}}\cdot l \cdot l = \tfrac{1}{2^{-\sqrt{l}}}\cdot l \cdot l
-2,820	10^{1 / 2} + 40^{1 / 2} = (4*10)^{1 / 2} + 10^{\frac{1}{2}}
-29,609	\frac{\mathrm{d}}{\mathrm{d}y} (2y^4) = 2\frac{\mathrm{d}}{\mathrm{d}y} y^4 = 2*4y^3 = 8y^3
-20,485	\frac55\frac{1}{-n + 9}(n + 5) = \tfrac{1}{-5n + 45}(5*n + 25)
-28,890	3 \cdot n = n + 2 + n + 2 \cdot (-1) + n
13,135	-(-y)^{k + 1} = -\left(-1\right)^{k + 1} \cdot y^{k + 1} = (-1)^{k + 2} \cdot y^{k + 1}
1,301	(C_2 - C_1)^2 = C_2^2 - C_2\cdot C_1\cdot 2 + C_1^2
7,879	\cos{4z} = \cos(\pi - 16 z) = -\cos{16 z}
26,441	2(-1) + s s = (-\sqrt{2} + s)*(\sqrt{2} + s)
8,212	2^k*((-1) + 2^{l - k}) = -2^k + 2^l
5,321	b^2 + b * b - bh2 + h^2 = h^216\Longrightarrow 0 = 2b^2 - 2bh - h^2*15
9,311	(\frac{1}{2} (B + 1))^2 = \left(B^2 + 1\right)/4 + 2 B/4 = (B + 1)/2
16,385	\frac12 \sin\left(2 f\right) = \sin(f) \cos\left(f\right)
-823	5401/10000 = 0 + \dfrac{5}{10} + \dfrac{4}{100} + 0/1000 + \frac{1}{10000}
-2,660	\sqrt{16} \sqrt{11} + \sqrt{11} = 4\sqrt{11} + \sqrt{11}
1,817	\dfrac{1}{81}*16 = \tfrac{2^4}{3^4}
9,361	E[AU] = 0 = 0E[U] = E[A] E[U]
30,054	\frac{1}{2*5} = 0.1
-10,622	\dfrac{J \cdot 5 + 5 \cdot \left(-1\right)}{8 \cdot J + 12} \cdot 3/3 = \frac{15 \cdot \left(-1\right) + 15 \cdot J}{J \cdot 24 + 36}
8,785	Vxy = xVy
25,968	V \cdot 4\% = 0.04 V
39,850	0 = \frac12 \cdot (1 + (-1))
14,977	Vk = kV
17,750	\left(y + 3\left(-1\right)\right)^2 + 9(-1) = -6*y + y^2
25,786	d/dz \sqrt{z^2} = \frac{2}{2\sqrt{z^2}}z
-10,509	-\frac{4x}{x12 + 12(-1)} = \frac{1}{4}4(-\frac{x}{3(-1) + 3*x})
18,212	\cos\left(f\right)\cdot \sin(y) + \sin(f)\cdot \cos(y) = \sin(f + y)
19,302	(z_1 + z_2)^2 - \left(-z_1 + z_2\right)^2 = 4 \cdot z_2 \cdot z_1
11,023	n^3 + (-1) = (\left(-1\right) + n) \cdot (n^2 + n + 1)
-20,149	5/5 \cdot \frac{1}{8 + q} \cdot \left(8 + q \cdot 6\right) = \frac{1}{5 \cdot q + 40} \cdot \left(q \cdot 30 + 40\right)
-19,626	\frac{8 \cdot 1/3}{7 \cdot \frac15} = \dfrac{5}{7} \cdot \dfrac83
25,314	42 = 84 + 42*(-1)
5,434	B - Y = B \cap Y^c = B \cap (B^c \cup Y^c) = B \cap B \cap Y^c = B - B \cap Y
-20,825	\frac{7}{7}\cdot \frac{1}{(-1) + m}\cdot \left(m\cdot (-4)\right) = \frac{1}{7\cdot m + 7\cdot (-1)}\cdot (\left(-28\right)\cdot m)
3,526	12-3(x+9)^2=0 \implies (x+9)^2=4 \implies x+9=\pm2 \implies x=-7,-11
24,527	3 * 3 = 22 2 + 1
28,709	-\frac1K + \frac{1}{K + (-1)} = \frac{1}{K^2 - K}
21,756	d/dz \tan^{-1}\left(z\right) = \frac{1}{z \cdot z + 1}
6,760	\cos{z} \sin{G} + \cos{G} \sin{z} = \sin(z + G)

-20,981

\frac{1}{10 + p} \cdot 1 = \frac{1}{p \cdot 10 + 100} \cdot 10

32,948

\sin^6{z} = (\sin^2{z})^3 = (1 - \cos^2{z}) * (1 - \cos^2{z}) * (1 - \cos^2{z})

24,435

25^x = (1 + 24)^x

10,498

2 + z = \frac{1}{z + 2(-1)}(z^2 + 4(-1))

-9,192

-2 \cdot 2 \cdot 3 - q \cdot 2 \cdot 2 \cdot 2 \cdot 3 = 12 \cdot (-1) - 24 \cdot q

5,607

\frac{\partial}{\partial x} u^n = u^{\left(-1\right) + n}*\frac{\mathrm{d}u}{\mathrm{d}x}*n

42,282

1.2 = 0.3 \cdot 4

-5,732

\frac{4}{5 \cdot (-1) + 5 \cdot q} = \frac{4}{((-1) + q) \cdot 5}

22,967

2n - (-1) + n = n + 1

28,633

I = \frac{I^2}{I}

31,225

2520 = 3 \cdot 3\cdot 2^3\cdot 5\cdot 7

11,569

a \cdot x = \dfrac{1}{1/a \cdot 1/x} = \frac{1}{\frac1x \cdot \frac{1}{a}} = x \cdot a

-11,879

3.276*0.1 = 3.276/10

1,779

a^{\frac32} = a^{\frac{1}{2}} (a^{\frac12})^2

-4,520

y^2 - 6*y + 5 = ((-1) + y)*(y + 5*(-1))

1,655

\lambda*\pi = \pi*n \Rightarrow \lambda = n

44,351

\frac{π}{1} = π

12,994

A_1 = 1\Longrightarrow \mathbb{E}[A_1] = 1

45,287

\frac25 = \dfrac15*2

25,254

{n + (-1) \choose (-1) + k}*\frac{n}{k} = {n \choose k}

-1,585

2\cdot \pi - \frac{1}{12}\cdot \pi = 23/12\cdot \pi

9,502

(-3/2 + 2)^2 = (-\frac12 \cdot 3 + 1)^2

19,290

\sqrt{2}/2 + \frac{\sqrt{2}}{2} \cdot i + \frac{\sqrt{2}}{2} - \sqrt{2} \cdot i/2 = \sqrt{2}

11,000

\frac{1}{A - B} = \frac{1}{(1 - \frac{B}{A}) \cdot A}

33,112

\frac{1}{2}\cdot (\left(-1\right) + 11) = 5

19,478

x + 2 = \frac12 \cdot (x \cdot 2 + 4 \cdot (-1)) + 4

10,254

(y + z) * (y + z) = y^2 + z^2 + 2*z*y

32,440

3\cdot \left(-1\right) + 2\cdot n = 2\cdot \left((-1) + n\right) + 3\cdot (-1) + 2

-9,632

0.01\cdot (-10) = -\dfrac{10}{100} = -\frac{1}{10}

5,110

4 \dfrac12 \left(p + 3\right) \frac12 (7 (-1) + p) = (3 + p) \left(7 \left(-1\right) + p\right)

-26,636

16 \cdot x^2 - y^2 \cdot 49 = (4 \cdot x + 7 \cdot y) \cdot (4 \cdot x - y \cdot 7)

-3,536

35/100 = \frac{1}{20\cdot 5}\cdot 35

387

57 \times 6 + 1 = 343 = 7^3

10,329

(1 + n)^3 = 1 + n^3 + 3 \cdot n \cdot n + 3 \cdot n

17,419

r \cdot r + r\cdot (-r + a) + \left(b - r\right)\cdot r = (a + b - r)\cdot r

-20,913

\dfrac99\cdot \frac{1}{2\cdot x + 8\cdot (-1)}\cdot (x\cdot (-4)) = \dfrac{1}{72\cdot (-1) + 18\cdot x}\cdot (x\cdot (-36))

-20,032

\frac{1}{5\cdot \left(-1\right) + r\cdot 10}\cdot (5\cdot (-1) + r\cdot 10)\cdot \frac{1}{7}\cdot 10 = \frac{100\cdot r + 50\cdot (-1)}{r\cdot 70 + 35\cdot (-1)}

-26,500

81 \cdot x^2 + 180 \cdot x + 100 = (x \cdot 9)^2 + 2 \cdot 9 \cdot x \cdot 10 + 10^2

12,979

(-1) + p + x = 1 + x + (-1) + p + (-1)

-20,485

\frac{5 + n}{9 - n} \dfrac55 = \tfrac{1}{-n \cdot 5 + 45} (25 + n \cdot 5)

-20,061

-\frac11 \cdot 3 \cdot \tfrac{\left(-8\right) \cdot p}{p \cdot (-8)} = \frac{24 \cdot p}{(-8) \cdot p}

-3,394

-\sqrt{16}\cdot \sqrt{6} + \sqrt{25}\cdot \sqrt{6} = \sqrt{6}\cdot 5 - 4\cdot \sqrt{6}

6,736

(ha + 1) \cdot (ha + 1) = a^2 h^2 + 2ha + 1

19,936

\frac{14}{7} = \frac77 \cdot 2

30,446

e^{6\eta} \eta = 1 \Rightarrow \eta \approx 0.2387

24,727

\frac{1}{3}\cdot 2 = \frac12 + \dfrac13 - \dfrac{1}{6}

-28,922

7/(7\cdot \frac{1}{20}) = 7\cdot \frac{20}{7} = 20

1,638

(x^3 \cdot x^9)^2 = x^{24}

28,870

A\cdot D = D\cdot B \implies 2\cdot A\cdot D = A\cdot B

-4,182

\frac{1}{x \cdot 24} \cdot x^5 \cdot 48 = \frac{x^5}{x} \cdot \frac{1}{24} \cdot 48

-428

-\pi \cdot 8 + \frac{115}{12} \cdot \pi = 19/12 \cdot \pi

20,208

2\cdot π - \frac{9}{5} - π\cdot 2 - \frac15\cdot 8 = -\dfrac{1}{5}

10,233

b^3 = 2 + 11\cdot i + 2 - 11\cdot i + 3\cdot \left((2 + 11\cdot i)\cdot (2 - 11\cdot i)\right)^{\dfrac{1}{3}}\cdot b = 4 + 15\cdot b

1,404

5(y + 9) (y + 2(-1)) (3(-1) + y) = y \cdot y \cdot y\cdot 5 + y^2\cdot 20 - y\cdot 195 + 270

34,763

1^2 + 40 \cdot 40 = 42^2 + 163 (-1)

-29,573

\tfrac{z^4*5}{z}*1 = 5*z^3

-15,594

\frac{(m^5)^3}{(m^5\cdot y^3) \cdot (m^5\cdot y^3) \cdot (m^5\cdot y^3)} = \frac{m^{15}}{m^{15}\cdot y^9}

9,781

\frac14 = \cos(2 \cdot 0)/4

36,958

2^{x + 1} = 2.2^x \gt x \cdot x + x \cdot x

30,405

7^{62} = 7^{64}/49 = 1/49 = 1/49

7,254

\frac{1}{11 + 17}17 \cdot 84 = 51

16,312

2^{\sqrt{l}}\cdot l \cdot l = \tfrac{1}{2^{-\sqrt{l}}}\cdot l \cdot l

-2,820

10^{1 / 2} + 40^{1 / 2} = (4*10)^{1 / 2} + 10^{\frac{1}{2}}

-29,609

\frac{\mathrm{d}}{\mathrm{d}y} (2y^4) = 2\frac{\mathrm{d}}{\mathrm{d}y} y^4 = 2*4y^3 = 8y^3

-20,485

\frac55*\frac{1}{-n + 9}*(n + 5) = \tfrac{1}{-5*n + 45}*(5*n + 25)

-28,890

3 \cdot n = n + 2 + n + 2 \cdot (-1) + n

13,135

-(-y)^{k + 1} = -\left(-1\right)^{k + 1} \cdot y^{k + 1} = (-1)^{k + 2} \cdot y^{k + 1}

1,301

(C_2 - C_1)^2 = C_2^2 - C_2\cdot C_1\cdot 2 + C_1^2

7,879

\cos{4z} = \cos(\pi - 16 z) = -\cos{16 z}

26,441

2*(-1) + s * s = (-\sqrt{2} + s)*(\sqrt{2} + s)

8,212

2^k*((-1) + 2^{l - k}) = -2^k + 2^l

5,321

b^2 + b * b - bh*2 + h^2 = h^2*16\Longrightarrow 0 = 2b^2 - 2bh - h^2*15

9,311

(\frac{1}{2} (B + 1))^2 = \left(B^2 + 1\right)/4 + 2 B/4 = (B + 1)/2

16,385

\frac12 \sin\left(2 f\right) = \sin(f) \cos\left(f\right)

-823

5401/10000 = 0 + \dfrac{5}{10} + \dfrac{4}{100} + 0/1000 + \frac{1}{10000}

-2,660

\sqrt{16} \sqrt{11} + \sqrt{11} = 4\sqrt{11} + \sqrt{11}

1,817

\dfrac{1}{81}*16 = \tfrac{2^4}{3^4}

9,361

E[AU] = 0 = 0E[U] = E[A] E[U]

30,054

\frac{1}{2*5} = 0.1

-10,622

\dfrac{J \cdot 5 + 5 \cdot \left(-1\right)}{8 \cdot J + 12} \cdot 3/3 = \frac{15 \cdot \left(-1\right) + 15 \cdot J}{J \cdot 24 + 36}

8,785

Vxy = xVy

25,968

V \cdot 4\% = 0.04 V

39,850

0 = \frac12 \cdot (1 + (-1))

14,977

V*k = k*V

17,750

\left(y + 3*\left(-1\right)\right)^2 + 9*(-1) = -6*y + y^2

25,786

d/dz \sqrt{z^2} = \frac{2}{2\sqrt{z^2}}z

-10,509

-\frac{4*x}{x*12 + 12*(-1)} = \frac{1}{4}*4*(-\frac{x}{3*(-1) + 3*x})

18,212

\cos\left(f\right)\cdot \sin(y) + \sin(f)\cdot \cos(y) = \sin(f + y)

19,302

(z_1 + z_2)^2 - \left(-z_1 + z_2\right)^2 = 4 \cdot z_2 \cdot z_1

11,023

n^3 + (-1) = (\left(-1\right) + n) \cdot (n^2 + n + 1)

-20,149

5/5 \cdot \frac{1}{8 + q} \cdot \left(8 + q \cdot 6\right) = \frac{1}{5 \cdot q + 40} \cdot \left(q \cdot 30 + 40\right)

-19,626

\frac{8 \cdot 1/3}{7 \cdot \frac15} = \dfrac{5}{7} \cdot \dfrac83

25,314

42 = 84 + 42*(-1)

5,434

B - Y = B \cap Y^c = B \cap (B^c \cup Y^c) = B \cap B \cap Y^c = B - B \cap Y

-20,825

\frac{7}{7}\cdot \frac{1}{(-1) + m}\cdot \left(m\cdot (-4)\right) = \frac{1}{7\cdot m + 7\cdot (-1)}\cdot (\left(-28\right)\cdot m)

3,526

12-3(x+9)^2=0 \implies (x+9)^2=4 \implies x+9=\pm2 \implies x=-7,-11

24,527

3 * 3 = 2*2 * 2 + 1

28,709

-\frac1K + \frac{1}{K + (-1)} = \frac{1}{K^2 - K}

21,756

d/dz \tan^{-1}\left(z\right) = \frac{1}{z \cdot z + 1}

6,760

\cos{z} \sin{G} + \cos{G} \sin{z} = \sin(z + G)