Equality Checker

Question 1

What is a mathematical equality? (Définition)

Answer

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

Question 2

How to check a mathematical equality?

Answer

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

Question 3

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 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.

Equality Checker