A selection of free math resources (calculators, exercises, games, quizzes, course reminders) that allow you to learn and practice algebraic calculus.

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.

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

- Quiz on algebraic calculus (algebraic calculation): This algebraic calculus quiz provides practice in using calculus techniques to simplify algebraic expressions.
- 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 derivative of the exponential function (algebraic calculation): This quiz on the exponential function allows you to practice using the techniques of calculating derivatives.
- 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 complex numbers (algebraic calculation): This quiz allows you to apply algebraic calculation techniques to complex numbers.
- Quiz on finding function antiderivatives (algebraic calculation): This quiz on mathematical functions allows you to practice using the techniques of finding antiderivatives.
- 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 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.
- Quiz solving equations with one unknown (algebraic calculation): This quiz on equations allows to practice solving different types of equations with one unknown.
- Quiz solving first degree equations (algebraic calculation): This quiz on first degree equations allows to practice solving simple equations with one unknown.
- 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 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.
- 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.
- 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.
- 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 statistics (algebraic calculation): This statistical calculations quiz allows you to practice calculating the mean and frequency of a series.
- Quiz on numerical sequences (algebraic calculation): This quiz allows you to practice different types of calculations that involve numerical sequences.
- Quiz on vectors (algebraic calculation): This quiz allows you to practice vector calculus: calculation of coordinates, norm, midpoint of a segment, dot product.

- Exercise 1239, develop an algebraic expression - algebraic calculus - expansion of algebraic expressions : This exercise allows to practice developing an algebraic expression by using different techniques of algebraic calculation.
- Exercise 1240, factoring an algebraic expression - algebraic calculus - expansion of algebraic expressions - factoring : This exercise allows to practice factoring an algebraic expression by using different techniques of algebraic calculation.
- Exercise 1325, simplifying a one-variable algebraic expression - expansion of algebraic expressions : This exercise allows you to practice the techniques of simplifying algebraic expressions that contain a single letter.
- Exercise 1326, expand an algebraic expression - algebraic calculus : The objective of this algebraic calculus exercise is to expand an algebraic expression.
- Exercise 1327, calculate an algebraic expression for given values - algebraic calculus : The objective of this exercise is to calculate an algebraic expression by replacing letters with a given value.
- Exercise 1328, comparison of fractions - comparisons of numbers, fractions, expressions - fractions : The objective of this solved exercise is to compare two fractions using the correct operator.
- Exercise 1336, first degree equation with one unknown of the form ax+b=c - solving equations - algebraic calculus - equations : The purpose of this exercise is to solve a linear equation of the first degree with one unknown of the form ax+b=c.
- Exercise 1337, equation of the first degree with one unknown form x+b=c - solving equations - algebraic calculus - equations : The purpose of this corrected exercise is to solve an equation with one unknown of the first degree of the form x+b=c.
- Exercise 1338, equation of the first degree with one unknown form ax+b=cx+d - solving equations - algebraic calculus - equations : The purpose of this corrected exercise is to solve an equation with one unknown of the first degree of the form ax+b=cx+d.
- Exercise 1339, solving an equation written in natural language - solving equations - algebraic calculus - equations : The purpose of this corrected math exercise is to solve an equation written in natural language.
- Exercise 1340, equations and percentages - solving equations - algebraic calculus - equations : The purpose of this exercise is to solve a numerical problem by calculating the percentage of a whole number.
- Exercise 1341, calculation of a percentage from two numbers - solving equations - algebraic calculus - equations : The purpose of this math exercise is to calculate a percentage from two numbers.
- Exercise 1342, calculation of a percentage from two given integers - solving equations - algebraic calculus - equations : The purpose of this math exercise is to determine a percentage from two given integers.
- Exercise 1412, develop an algebraic expression with a special expansion - algebraic calculation and remarkable identities : The purpose of this exercise is to develop an algebraic expression using the most suitable remarkable identity.
- Exercise 1413, develop the square of a number with a remarkable identity - algebraic calculation and remarkable identities : The purpose of this exercise is to calculate the square of a number using a remarkable identity.
- Exercise 1430, factoring an algebraic expression with squares - algebraic calculation and remarkable identities - numbers and equations - factoring : The purpose of this corrected algebraic calculus exercise is to factor an algebraic expression that involves squares.
- Exercise 1431, factoring a difference of squares - algebraic calculation and remarkable identities - numbers and equations - factoring : The purpose of this exercise is to factor an algebraic expression using a remarkable identity of the form a² - b².
- Exercise 1631, degree of a polynomial and algebraic calculation - polynomial functions : The purpose of this exercise is to practice developing a polynomial and determining its degree.
- Exercise 1632, degree of a polynomial and algebraic calculation using remarkable identities - polynomial functions : The goal of this exercise is to practice developing a polynomial with remarkable identities and determining its degree.
- Exercise 1633, factoring a polynomial of degree 3 - polynomial functions - factoring : The goal of this exercise of algebraic calculation is to factor a polynomial of degree 3 knowing one of its roots.
- Exercise 1634, calculating the roots of a polynomial of degree 3 - polynomial functions : The goal of this exercise of algebraic calculation is to determine the values for which a polynomial of degree 3 is equal to 0.

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