Algebra Calculators

Algebra homework tends to stall in the same places: an equation that will not rearrange, a matrix that will not resolve, or a log expression that looks different from the answer in the back of the book. The tools here work through those steps directly, showing the result for the values entered rather than explaining the topic in the abstract.

Solve a pair of linear equations the way your algebra class expects: isolate one variable, substitute it into the other equation, and work down to a single unknown.

Give this calculator any quadratic in standard form y = ax² + bx + c and it converts it to vertex form y = a(x − h)² + k, showing every…

Type any linear expression, like 3x + 5 – 2x + 7, and get the simplified form with each step shown.

Logarithms and exponents are two ways of saying the same thing.

Some matrices run out of ordinary eigenvectors: a repeated eigenvalue produces only one independent direction, and diagonalization stops there.

An unknown sitting in an exponent or inside a logarithm needs a different move from ordinary algebra: you undo the exponential with a logarithm, or undo the logarithm by exponentiating.

Evaluating an expression means working out its value by applying the order of operations correctly: parentheses first, then exponents, then…

An eigenvalue is the factor by which a matrix stretches one of its special directions: for a square matrix A, a nonzero vector v with Av = λv keeps its direction and is only scaled by λ.

Two linear equations in two unknowns have exactly one answer, no answer, or infinitely many, and which case you are in is decided by a single number: the determinant.

The fourth root of a number is the value that, multiplied by itself four times, gives the number back. It is also the square root of the square root.