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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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

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 make them 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, 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

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.

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Source : https://www.dcode.fr/equality-check

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