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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To check if 2 values 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.
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 different 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.