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Step-by-Step Solutions
Solutions for over 60 topics within math, chemistry and physics.
Arithmetic
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See how to perform basic arithmetic:
4 * 7
Check your work using step-by-step arithmetic:
60431 / 89
9 (3+1) + 17 / (6-12)
Follow the steps to convert an improper fraction to a mixed number:
87/5 as a mixed number
More examples
Statistics
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Perform basic statistical analysis on a set of data, seeing the steps along the way:
average of {1, 2, 3, 4, 5, 6, 7}
mode of {1, 5, 4, 2, 3, 4, 5, 11, 4, 11, 20}
variance 4, 6, 7, 9, 10, 11
quartile of {1, 2, 3, 4, 5, 6}
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Discrete Mathematics
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Find step-by-step solutions for prime factorization, primality testing, GCD and more:
is 73 prime?
lcm(90, 342)
are 12 and 21 coprime?
Follow the steps to convert between bases:
convert 33ab3653 base 12 to base 10
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Chemistry
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Get a step-by-step procedure to draw the Lewis structures of molecules:
What is the Lewis structure of NO2
Follow the steps for unit conversion:
convert 5mL benzene to moles
Learn how to balance a chemical reaction:
glucose + oxygen -> water + carbon dioxide
Compute oxidation states of chemicals:
oxidation states of chromium(III) chloride
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Algebra
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Solve equations one step at a time:
x^2 + 5x + 6 = 0
Factor polynomials step by step:
factor x^3+2x^2+x+2
Expand polynomials using FOIL, the binomial theorem and other methods:
expanded form of (x + 3)^2
Learn to rewrite a rational function using our step-by-step partial fraction decomposition:
partial fraction decomposition 1/(x^2 + 4x + 3)
More examples
Calculus
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Find the derivative using the product rule, chain rule and other methods:
derivative of x^4 + 9x^3 + 7x - 2
Calculate an integral by substitution, integration by parts and other methods:
integrate sin(x)cos(x)^2
Learn how to take a limit:
limit of (x - 3) / (x^2 - 2x - 3) as x approaches 3
Find local and global extrema using a variety of tests:
find the extrema of 3x^4 - 4x^3 - 12x^2 + 1
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Linear Algebra
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Compute properties of a matrix step by step:
{{2,4,4},{1,2,2},{0,7,3}}
Find the determinant step by step with various methods:
determinant of {{1,2,1}, {1,1,0}, {0,1,1}}
Compute eigenvalues and eigenvectors step by step:
eigenvalues {{3,-1},{0,2}}
Compute a cross product step by step:
(1,2,3)x(3,4,5)
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Physics Formulas
Do physics calculations step by step:
work W=30J, d=100m
photon energy 435nm
Geometry
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Compute properties of geometric objects step by step:
area of a circle with radius 2
Learn details of some geometric computations:
distance between (3, 2) and (5, 1)
slope of line through (2, 3) and (4, -1)
Determine the equation of a line with certain properties using a selected form:
equation of line through (2, 5), (4, 1)
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Differential Equations
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See how ordinary differential equations are solved:
solve y' = y^2 x
y'(t) - 2y(t) = 3 e^(2t)
t^2 y'(t) + 2t y(t) = t^4 y(t)^2 + 4
y''+ y = sin(2x)
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Proofs
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See the steps toward proving a trigonometric identity:
(1 + tan(x))/(1 - tan(x)) = (cos(x) + sin(x))/(cos(x) - sin(x))
Prove a sum identity by induction:
prove by induction sum of j from 1 to n = n(n+1)/2 for n>0
Prove divisibility by induction:
using induction, prove 9^n-1 is divisible by 4 assuming n>0
Prove an inequality by induction:
prove by induction (3n)! > 3^n (n!)^3 for n>0
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