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Examples for
Step-by-Step Algebra
Algebraic Substitutions
Evaluate an expression one step at a time:
evaluate x^2 + 2(x + 7) - 19 at x = 7
(x - 1)(x + 3)^2 + 7 where x = 2
evaluate x^2 y at (x,y) = (3,4)
Find the value of a function at a given point:
if f(x) = 2 * x + sqrt(4) - 2, what is f(1)?
g(5) for g(t) = t^2 + 5t - 6
Exponents
Multiply expressions with exponents:
x^5 x^7
simplify m^4 p m x m^2 x^3
Perform division with exponents one step at a time:
x^2/x^3
simplify b^(-5)/b^4
Get the steps for simplifying powers of exponents:
(x^2)^3
simplify (x^(-4))^(-2)
Rational Expressions
See how to add or subtract rational expressions:
simplify 2/x + 4/x + 5/x^2
simplify 1/(x+2) - 2/(x+2)
Perform multiplication of rational expressions step by step:
simplify 2/x * 3/x
simplify 1/(x-1) * (x-3)/(x-2)
Show how to simplify rational functions with common factors:
simplify (x-2)/((x-3)(x-2))
simplify ((t-5)(t+8))/((t-8)(t-5))
Simplify rational expressions with the steps provided:
simplify k/(k + 1) + 1/((k + 1) (k + 2))
Learn to rewrite a rational expression using partial fraction decomposition:
partial fraction decomposition 1/(x^2 + 4x + 3)
1/(x^3 + 4x^2 + 5x + 2) partial fractions
Solving Equations & Inequalities
Solve equations one step at a time:
solution to 2 * m - 3 = 1
2.1 x + 3.4 = 5.6 solve for x
solution set to x + y = y - 2 for x
find t for t^2 + 3t + 2 = 0
solve 4 * sin(t)^2 = 1
Investigate equations with rational expressions:
solve 2/x + 5 = 6
solutions (x^2 + 4x - 32)/(x - 4) = 0
Solve equations with absolute value over the reals:
solve 3|x| = 7 over reals
real solutions to 3|x-5/4| = |7-x|
Get step-by-step solutions for solving radical equations:
solve sqrt(n - 5) = 10
2 sqrt(x-3) = 8 solve for x
Learn how to solve exponential equations:
e^(5n) = 8 solve for n over reals
solve (9^(x + 1)) - (28 (3^(x))) + 3 = 0 over the real numbers
See the steps for solving linear inequalities:
solve -x + 5 < 3 + x
solve a - 2a + 1 <= 5a
Intercepts
Find
x
‐intercepts:
x intercept 3x+5
x intercepts of sin(x)
See the steps for finding the
y
‐intercept:
y intercept 2x+3
where does x^2+1 cross the y-axis?
show y-intercept for cos(x) + 3
Linear Expressions
Find the equations of lines defined by slopes and points:
line with slope 3 and y intercept 5
line through (2, 3) and (4, 5)
line passing through (0, 1) with slope 5
find line containing (2, 3) with y intercept 5
See the steps for solving linear equations using addition and subtraction:
solve x + 2 = 3
find the solutions to x + 5.7 = 2.4
Learn how to solve linear equations using multiplication and division:
solve -2x = 6
solve the equation x/3 = 10
Show the steps to solve linear equations with multiple operations:
solve 2 x + 3 = 6
what is x if 3x - 3 + 4 = 8
Solve linear systems with multiple methods:
x + y = 1, x - y = 3
solutions to the system 3x - y - z = 2, 2/3x + 5y = z, x - y = 3/4 z
Exponential Expressions
See how to solve exponential equations with complete steps:
solve e^x = 1 over the reals
solve 7*4^x + 5=33 over the reals
solve 2^(x+3) = 4 over the reals
Compute financial present and future values with steps:
present value continuous interest on $1000 at 8% over 5 years
RELATED EXAMPLES
Algebra
Equation Solving
Polynomials
Rational Functions
Simplification
Polynomial Expressions
See how to combine like terms:
simplify a + b + 2a + 3b + 3 + 4
show how to add 2 x - y + 3 x + 5 y
Show how to add polynomial expressions step by step:
(x - 2) + (x - 3)
simplify (x^2 + 2x + 3) + (x^2 + 3x + 4)
Subtract polynomial expressions:
simplify (x + 2) - (4x - 5)
simplify the expression (x^2 + 2x) - (x^2 + 3x + 5)
Show your work for multiplying polynomials:
expand (x+3)*(x-4)
multiply out (x^2+2x+3)(x^2+3x+4)
expand (x^2+2x)(x+6)
multiply out (x^2+2x+3)(x^2+3x+4)(x+3)
Perform polynomial long division step by step:
(x^4 - 3 x^3 + 5 x^2 - 11 x - 12)/(x - 3) long division
(y^5 + y^4 - 6y^2 + 8)/(y^3 + y - 7) quotient and remainder
Expand polynomials using the distributive law, the binomial theorem and other procedures:
expanded form of (x + 3)^2
simplify 5(x^2 + 2x + y^2)
Factor out the greatest common divisor:
factor 3x + 3y + 3z
factor x^2 + x^3 + x^5
Use the difference of squares method to factor binomials:
factor x^2 - 9
factor x^2 - 81
Choose from multiple methods to complete the square:
complete the square x^2 + 2x + 3
complete the square x^2 + y^2 + 2x + 4y - 11
Factor expressions as a sum or difference of cubes:
factor x^3 + 8
x^3 - 1 factored form
Factor polynomials step by step:
factor 2x^2 + 4x + 6
factored form of x^3 - 8
factorization of x^4+4
factor x^3+2x^2+x+2
Find zeros of a quadratic expression by factoring, completing the square or applying the quadratic formula:
zeros of x^2+2x + 3
solve x^2 + 2x -3 = 0
roots of x^2 - 2x + 1
Find candidate roots using the rational root theorem:
rational solutions of x^3 - 3x + 2
solve 6 x^3 - 3x^2+3x + 27 over rationals
Compute the degree of a polynomial with steps:
What is the degree of x^2+1?
compute the degree of x^2yz-x^5
find the degree of the polynomial (1+xy) (x+y) (z^2-3)
Logarithmic Expressions
See how to simplify log expressions with steps:
simplify log(2x)
simplify log(2*3)
simplify log(2 x y z /w)
simplify log(2x^2)
See how to combine multiple logarithmic expressions into a single logarithm with steps:
simplify log(2)+log(3)
simplify log(x)+log(y)+log(z)+log(w)
simplify 2 log(x)
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