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Step-by-Step Solutions

Solutions for over 200 topics within math, chemistry and physics problems across all levels of education, from elementary school to college.

Step-by-Step Solutions

See how to perform basic arithmetic:

Check your work using step-by-step arithmetic:

9 (3+1) + 17 / (6-12)

Follow the steps to convert an improper fraction to a mixed number:

87/5 as a mixed number

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}

Discrete Mathematics ›

Find step-by-step solutions for prime factorization, primality testing, GCD and more:

are 12 and 21 coprime?

Follow the steps to convert between bases:

convert 33ab3653 base 12 to base 10

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

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)

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

Linear Algebra ›

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)

Do physics calculations step by step:

average velocity, 2 miles over 20 minutes

Doppler shift for sound at source frequency 100 kHz for 70 mph

coulomb's law for 0.1 C and 0.2 C at 2 meters distance

first law of thermodynamics Q=-1150 J, W=-480 J

Snell's law for air and water, angle of incidence of 10 degrees

length contraction for a proper length of 1 yard at 0.93c

parallax distance for 0.3 arcseconds

photon energy 435nm

water flow through a pipe 2" diameter, 10' length of pipe with 2 kPa pressure difference

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)

Differential Equations ›

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)

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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