Equality Checker

Question 1

How to check a mathematical equality?

Answer

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.

dCode displays TRUE or FALSE when checking mathematical identities / equalities, use the equation solver or the inequality solver for more detailes calculations.

Question 2

How to rewrite a mathematical expression?

Answer

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.

Equality Checker