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.
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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