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Examples for

Step-by-Step Algebra

Evaluation

Evaluate an expression at a point one step at a time:

evaluate x^2 + 2(x + 7) - 19 at x = 7
(x - 1)(x + 3)^2 + 7 where x = 2

Systems of Linear Equations

Solve linear systems with multiple methods:

x + y = 1, x - y = 3
solve 3x - y - z = 2, x + 2y - 3z = -12, 2x + y + 3z = 9

Intercepts

Find axis intercepts one step at a time:

x intercepts of sin(x)
y intercept of x^2+1
intercepts of (x^2+2)(x^2-1)

Equation Solving

Solve equations one step at a time:

solution to 2x - 3 = 1
x^2 + 5x + 6 = 0
solve (9^(x + 1)) - (28 (3^(x))) + 3 = 0 over the real numbers
solve sin(t) + cos(t) = 1

Find candidate rational roots of a polynomial:

rational solutions of x^3 - 3x + 2

Polynomials

Factor polynomials step by step:

factor x^3 - 8
factorization of x^4+4
factor x^3+2x^2+x+2

Expand polynomials using the distributive method, the binomial theorem and other procedures:

expanded form of (x + 3)^2
multiply out (x^2 + x)^4
expand (x^2 + 5x + 8)*(x - 4)

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 = 0

Perform polynomial long division:

(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

Trigonometric Functions

Expand trigonometric expressions with the steps provided:

simplify sin(x + pi/4)
expand cos(2x)^2
sin(x+y+z)
cos(2x)^2 + sin(2x)

RELATED EXAMPLES

  • Algebra
  • Equation Solving
  • Polynomials
  • Rational Functions
  • Simplification

    • Rational Functions

    Simplify rational expressions with the steps provided:

    simplify (1/a + 1/b) (a + b)
    k/(k + 1) + 1/((k + 1) (k + 2))

    Learn to rewrite a rational function using our step-by-step partial fraction decomposition:

    partial fraction decomposition 1/(x^2 + 4x + 3)
    1/(x^3 + 4x^2 + 5x + 2)
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