**Algebraic calculus** is a form of calculation that combines letters, numbers, and operations.
The calculators, quizzes, games and exercises offered here allow you to practice algebraic calculus online.

- Calculation of the monthly payments of the insurance of a credit : loan_insurance. Credit insurance monthly payment calculator: real estate credit, consumer credit, and other types of credit.
- Algebra calculator : calculator. Calculator that allows to make algebraic calculation by combining operations with letters and numbers, and to indicate the steps of calculation
- Simplifying surds calculator : simplify_surd. Online surds calculator that allows you to make calculations in exact form with square roots: sum, product, difference, ratio.
- Trigonometric Calculator : simplify_trig. Calculator wich uses trigonometric formula to simplify trigonometric expression.
- List of calculations applicable to an algebraic expression : possible_calculations_with. Return the list of calculations that can be done on an algebraic expression
- Calculation of binomial coefficients : binomial_coefficient. A binomial coefficient calculator that allows you to calculate a binomial coefficient from two integers.
- Partial fraction decomposition calculator : partial_fraction_decomposition. The calculator allows a rational fraction to be broken down into simple elements.
- Derivative calculator : derivative. The derivative calculator allows steps by steps calculation of the derivative of a function with respect to a variable.
- Taylor expansion calculator : taylor_series_expansion. The taylor series calculator allows to calculate the Taylor expansion of a function.
- Logarithmic expansion : expand_log. The calculator makes it possible to obtain the logarithmic expansion of an expression.
- Trigonometric expansion : expand_trigo. The calculator makes it possible to obtain the trigonometric expansion of an expression.
- Expand calculator : expand. Calculator is able to expand an algebraic expression online and remove unnecessary brackets.
- Expand and simplify an algebraic expression online : expand_and_simplify. Online calculator that allows you to expand and reduce an algebraic expression.
- Factoring calculator : factor. The factoring calculator allows to factor an algebraic expression online with steps.
- Integral calculator : integral. The integral calculator calculates online the integral of a function between two values, the result is given in exact or approximated form.
- Indefinite integral calculator : antiderivative. The antiderivative calculator allows to calculate an antiderivative online with detail and calculation steps.
- Limit calculator : limit. The limit calculator allows the calculation of the limit of a function with the detail and the calculation steps.
- Trigonometric linearization : linearization_trigo. Calculator that allows to linearize a trigonometric expression.
- Calculation of the monthly payments of a loan : monthly_loan. Loan monthly payment calculator : home loan, consumer loan, and other types of loan.
- Scientific online calculator : evaluate. Online Scientific Calculator to calculate algebraic expressions and get a numerical result.
- Simplify Calculator : simplify. Calculator wich can simplify an algebraic expression online.

- Quiz solving equations of the second degree (algebraic calculation) : This quiz on the equations of the second degree allows to practice the methods of resolution based on the use of the discriminant.
- Quiz solving equations with one unknown (algebraic calculation) : This quiz on equations allows to practice solving different types of equations with one unknown.
- Quiz derivative of the exponential function (algebraic calculation) : This quiz on the exponential function allows you to practice using the techniques of calculating derivatives.
- Quiz on complex numbers (algebraic calculation) : This quiz allows you to apply algebraic calculation techniques to complex numbers.
- Quiz solving inequalities with one unknown (algebraic calculation) : This math quiz on inequations allows you to practice solving different types of inequations with one unknown.
- Quiz on calculating with square roots (algebraic calculation) : This math functions quiz provides practice in using square root calculation techniques
- Game expression expansion (algebraic calculation) : The goal of this game is to develop an algebraic expression. To win this quiz, all you have to do is find the correct expansion of the expression from a list.
- Quiz derivative of logarithm function (algebraic calculation) : This quiz on the logarithm function allows you to practice using the techniques of calculating derivatives
- Quiz on the calculation of the derivative of a function (algebraic calculation) : This quiz on mathematical functions allows you to practice using the techniques of calculating derivatives.
- Quiz number of solutions of the second degree equation (algebraic calculation) : The goal of this quiz on 2nd degree equations is to find the number of solutions of a quadratic equation using the discriminant.
- Factorization game using remarkable identities (algebraic calculation) : This game uses the remarkable identities to factor an algebraic expression. The goal is to find the factorized form of the expression in a list.
- Expression factoring game (algebraic calculation) : The goal of this game is to factor an algebraic expression. To win this quiz, you just have to find the right factorization of the expression in a list.
- Quiz solving first degree equations (algebraic calculation) : This quiz on first degree equations allows to practice solving simple equations with one unknown.
- Quiz on finding function antiderivatives (algebraic calculation) : This quiz on mathematical functions allows you to practice using the techniques of finding antiderivatives.
- Quiz on algebraic calculus (algebraic calculation) : This algebraic calculus quiz provides practice in using calculus techniques to simplify algebraic expressions.
- Quiz calculating the discriminant of a polynomial (algebraic calculation) : This quiz on the calculation of the discriminant of a polynomial allows you to prepare yourself for the solution of second degree equations.

Algebraic calculus is a form of calculus that combines letters, numbers, and operations. The following formulas can be used in factoring and expanding algebraic expressions.

#### Formulas

- ka+kb=`k*(a+b)`
- ka-kb=`k*(a-b)`
#### Special expansions

- `(a+b)^2=a^2+2*a*b+b^2`
- `(a-b)^2=a^2-2*a*b+b^2`
- `(a-b)*(a+b)=a^2-b^2`
#### Factoring by (x-a)

Let a, b and k be three numbers we have :

Let a,b be two numbers we have the following three equalities: :

P is a polynomial, a a real. If P(a)=0, then P is factorizable by (x-a). That is, there exists a polynomial Q such that for all x, P(x)=(x-a)Q(x).

To simplify a literal expression, we group the dependent terms depending on the same letters and then we reduce each grouping, as in this example: x+x+3y-2y=2x-y.

Geometry | Matrices | Numbers | Vectors | Statistics | Trigonometric functions | Fractions | Complex numbers | Algebraic calculation | Real functions | Numerical sequences | Equations