Examples for
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.
See how to show your work for arithmetic problems.
See step-by-step solutions for doing basic multiplication or division problems:
3 × 560431 / 89See the steps for applying the order of operations for arithmetic:
9 (3+1) + 17 / (6-12)Follow the steps to convert an improper fraction to a mixed number:
87/5 as a mixed numberSee the steps for analyzing data and applying statistical methods.
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, 11quartile of {1, 2, 3, 4, 5, 6}Explore step-by-step solutions for solving equations involving derivatives.
See how ordinary differential equations are solved:
solve y' = y^2 xy'(t) - 2y(t) = 3 e^(2t)t y(t) (1 + t y(t)^2) y'(t) = 1y''+ y = sin(2x)Get step-by-step results for proving mathematical statements.
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>0Prove an inequality by induction:
prove by induction (3n)! > 3^n (n!)^3 for n>0Investigate the convergence or divergence of an infinite sum step by step:
Does the sum of 5*3^(1 - n) converge?Learn how to manipulate and solve expressions with variables step by step.
Solve equations one step at a time:
find t for t^2 + 3t + 2 = 0Factor polynomials step by step:
factor x^3+2x^2+x+2Expand polynomials using the distributive law, the binomial theorem and other procedures:
expanded form of (x + 3)^2Learn to rewrite a rational expression using partial fraction decomposition:
partial fraction decomposition 1/(x^2 + 4x + 3)Learn the steps for evaluating or manipulating trigonometric expressions.
Show your work for solving the unknown measurements of a triangle:
right triangle with hypotenuse 2, A = 60 degreesSee the steps for how to find the values of a trigonometric function:
sin(2pi/3)Get step-by-step solutions for applying the sum and difference formulas:
simplify sin(x-y) + sin(x+y)See the steps involved for determining different properties of numbers.
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 10Explore a wide array of chemistry topics with step-by-step solutions.
Get a step-by-step procedure to draw the Lewis structures of molecules:
What is the Lewis structure of NO2Follow the steps for unit conversion:
convert 5mL benzene to molesLearn how to balance a chemical reaction:
glucose + oxygen -> water + carbon dioxideCompute oxidation states of chemicals:
oxidation states of chromium(III) chlorideExplore two- and three-dimensional shapes and their properties.
Compute properties of geometric objects step by step:
area of a circle with radius 2find the surface area of a sphere with radius = 8Learn how to compute different properties for graphical objects:
(2, -4, 7) to (-4, 6, 1) distanceexpress x^2+y^2=3 in polar coordinatesDetermine the equation of a line with certain properties using a selected form:
equation of line through (2, 5), (4, 1)Get step-by-step solutions for common calculus problems, like computing limits, derivatives and integrals.
Find the derivative using the product rule, chain rule and other methods:
compute the derivative of x*sin[x]Calculate an indefinite integral by substitution, integration by parts and other methods:
integrate sin(x)cos(x)^2Learn how to take a limit:
limit of (x - 3) / (x^2 - 2x - 3) as x approaches 3Explore step by step a variety of tests to discover local and global extrema:
find the extrema of 3x^4 - 4x^3 - 12x^2 + 1Solve problems involving vectors and matrices step by step.
Compute properties of a matrix step by step:
{{2, 2^2, 8/4}, {1, - 4, 7 - 4}}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)See how to solve physics problems step by step.