Question

Which of the following statements has an error in it?
A) $5x + 3x = 8x$
B) $8{x^2} + 2 = x\left( {8{x^2} + 2} \right)$
C) $6x - 12 = 6\left( {x - 2} \right)$
D) ${x^2}{y^2} - xy = xy\left( {xy - 1} \right)$

Answer 1

Hint:
We will verify every option to check if the given equations are justified or not. We will simplify the equations to check if the left hand side of the equation is equal to the right hand side of the equation or not. If there is any equation in which both of the sides aren’t equal, then we will say that equation has an error in it.

Complete step by step solution:
We need to find which of the given options has an error in them. We will check the given statements (equations) individually to verify them.
Option (A): $5x + 3x = 8x$
This equation is simple and can be verified just by observation that it is true since in this equation LHS: $5x + 3x = 8x = {\text{RHS}}$.
Hence, option (A) is correct and there is no error in it.
Option (B): $8{x^2} + 2 = x\left( {8{x^2} + 2} \right)$
In this equation, we will consider the right hand side of the equation and simplify it as:
$RHS:x\left( {8{x^2} + 2} \right) = 8{x^3} + 2x \ne LHS$. Therefore, this equation is not true.
Hence, option (B) is incorrect and it has errors in its statement.
Option (C): $6x - 12 = 6\left( {x - 2} \right)$
Considering and simplifying the right hand side of the equation, we get
$ \Rightarrow RHS:6\left( {x - 2} \right) = 6x - 12 = LHS$ .
Therefore, the option (C) is correct without any error.
Option (D): ${x^2}{y^2} - xy = xy\left( {xy - 1} \right)$
We will consider the right hand side of the equation and simplify it as:
$ \Rightarrow RHS:xy\left( {xy - 1} \right) = {x^2}{y^2} - xy = LHS$

Therefore, option (D) is correct.

Note:
In this question, we were required to check if the given statements were true or not. So, we have verified the equations by equating their left and right hand side equal to each other. These all are algebraic expressions which are defined as the expressions which are formed by variables with different powers, integer constants and algebraic operations such as addition, subtraction, etc.