How do you simplify $\left(x+2 \right)+\left(x-2 \right)\left( 2x+1 \right)$?

Hint: To solve the above problem firstly we will apply Distributive Property $a\left( b+c \right)=ab+ac$in the given equation. So now the question is that what is the meaning of distributive property that means according to above formula it is applicable for Multiplication, for it we multiply x to (2x+1) and (-2) to (2x+1).then we arrange the like term And make necessary calculations to get the required result.

Complete step by step solution:
Now we solve the above equation
$\Rightarrow \left( x+2 \right)+\left( x-2 \right)\left( 2x+1 \right)................\left( 1 \right)$
We apply distributive property in equation (1)
According to distributive property when a factor is multiplied by the sum of two terms, it is essential to multiply each of the two numbers by the factor and finally perform the addition operation. This property can be stated symbolically as:
A (B+C) =AB+AC
That is
$\Rightarrow \left( x+2 \right)+x\left( 2x+1 \right)-2\left( 2x+1 \right)$
Now we will open the parenthesis and multiply $x$ to $\left( 2x+1 \right)$ and -2 to $\left( 2x+1 \right)$
$\Rightarrow (x+2)+2{{x}^{2}}+x-4x-2$
Now we eliminate redundant parentheses and rewrite the equation
$\Rightarrow x+2+2{{x}^{2}}+x-4x-2$
Now we combine like terms and make necessary calculations
$\Rightarrow 2{{x}^{2}}+x+x-4x+2-2$
Here we know that 2-2 is 0 and x+x becomes 2x
$\Rightarrow 2{{x}^{2}}+2x-4x+0$
Now we subtract 2x-4x so it becomes -2x
$\Rightarrow 2{{x}^{2}}-2x$
Now we take \[2x\] common from both the term
\[\Rightarrow 2x(x-1)\]
This is the solution of the above equation
\[2x(x-1)\]

Note: When we get this type of problem, we should always try to make the necessary calculations in the given equation to get the final solution. While performing calculations we should not confuse with sign convention. Since sign is important in such a type of problem.