Tool to check an equality between 2 mathematical expressions (written in different forms, factored, expanded etc.). Checker with or without unknown values / variables.
Equality Checker - dCode
Tag(s) : Symbolic Computation
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Equality Checker
Equality Checker
Answers to Questions (FAQ)
What is a mathematical equality? (Définition)
In mathematics, an equality is a set of two expressions (or more), connected by the symbol = (equal), which is true if and only if the result of each side of the equal sign is identical.
Example: $ 1 + 3 = 2 + 2 $ is an equality
How to check a mathematical equality?
To check if 2 values or functions or mathematical expressions are equal or not, it is necessary to transform their writing (via calculations, simplifications, developments or factorizations) in order to compare them and assess whether they are identical.
Example: Check that $ (a+b)(a-b) = a^2 - b^2 $ is to calculate $ (a+b)(a-b) = a^2 - a*b + b*a - b^2 = a^2 - b^2 $ so the 2 writings are equivalent which means that the 2 expressions are equal.
dCode's equality checker displays ✔ (true) or ✘ (false) when checking mathematical identities/equalities/equivalences, use the equation solver or the inequality solver for more detailed calculations.
It is also possible to check if the difference (subtraction) between the two expressions is equal to 0.
Example: $ 1 + 3 - (2 + 2) = 0 $ so $ 1 + 3 = 2 + 2 $ is a verified equality
Some equalities are only true under certain variable conditions.
Example: $ \ln(a*b) = \ln(a)+\ln(b) $ only if $ a $ and $ b $ are positive real numbers.
How to rewrite a mathematical expression?
To rewrite a mathematical expression, there are several techniques:
— mathematical development which consists in breaking down the multiplications or products a sum or a difference of values.
Example: $ 2 \times (x+1) = 2x+2 $
— mathematical factorization which consists of transforming the sums or differences into multiplication or products of values
Example: $ 3y+9 = 3(y+3) $
— mathematical simplification which consists of removing redundant or unnecessary values (which cancel each other out)
Example: $ 2a + 2b -a -b -a = 2a-a-a + 2b-b = b $
For a quick rewrite, make maximum use of mathematical knowledge, remarkable identities, known products etc. to facilitate comparison
What is the difference between an equation and an equality?
A mathematical equality is a relationship between two expressions indicating that they are equivalent, while an equation is also a mathematical equality but containing an unknown/variable to be solved whose value is sought in order to make the equality true.
Source code
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