Find and correct errors of the following mathematical expression:
$3x + 2x = 5{x^2}$.

Hint: In the given problem, to find errors first we will simplify the LHS term and compare it with the RHS term. For this, we will use basic knowledge of addition.

Complete answer:
In this problem, the mathematical expression $3x + 2x = 5{x^2} \cdots \cdots \left( 1 \right)$ is given. We have to find and correct the errors in this expression. For this, first we will simplify the LHS term. The LHS term of the equation $\left( 1 \right)$ is $3x + 2x$. Here we can see that $x$ is the common variable. Let us take $x$ common out of the LHS term. Therefore, we can write
LHS $ = x\left( {3 + 2} \right) = x\left( 5 \right) = 5x$
From the equation $\left( 1 \right)$, we can say that the RHS term is $5{x^2}$. Now we have the LHS term is $5x$ and the RHS term is $5{x^2}$. So, we can say that LHS is not equal to RHS. If the RHS term of given expression is $5x$ then we can say that given expression is true. Therefore, the correct mathematical expression is $3x + 2x = 5x$.

Note: A mathematical expression must be well-defined. It is not necessary that a mathematical expression must include variables. For example, $2 + 3 = 5$ is a mathematical expression and we can see that there is no variable in this expression. If there are a minimum of two terms and one mathematical operation in the expression then we can say that it is a mathematical expression. In the given problem, $x$ is the variable and variable usually denoted by letter. In this problem, the given expression can be written in words as “sum of two terms $3x$ and $2x$ is $5{x^2}$” but this is not the correct (valid) expression. The correct expression can be written in words as “sum of two terms $3x$ and $2x$ is $5x$”.