How do you simplify $3{{w}^{2}}{{v}^{6}}-6{{w}^{3}}v+9{{w}^{3}}v+2{{w}^{3}}v-9{{w}^{2}}{{v}^{6}}$ ?

Hint: In this question, we have to simplify the given algebraic expression. Thus, we will use the basic mathematical rule to get the solution. As we know, in the given expression, we have only two variables w and v. Thus, we will first take w and v common from the given algebraic expression. Then, we will use the basic mathematical rule by subtracting or adding the like terms. After that we will use the distributive property $a(b-c)=ab-ac$ in the expression, to get the required result for the solution.

Complete step by step solution:
According to the question, we have to simplify the given algebraic expression.
Thus, we will use the basic mathematical rules to get the solution.
The algebraic expression given to us is $3{{w}^{2}}{{v}^{6}}-6{{w}^{3}}v+9{{w}^{3}}v+2{{w}^{3}}v-9{{w}^{2}}{{v}^{6}}$ ---------- (1)
Now, we will take the common v and w from the each term of the equation (1), we get
$\Rightarrow wv\left( 3{{w}^{1}}{{v}^{5}} \right)-wv\left( 6{{w}^{2}} \right)+wv\left( 9{{w}^{2}} \right)+wv\left( 2{{w}^{2}} \right)-wv\left( 9{{w}^{1}}{{v}^{5}} \right)$
Now, we will again take common $wv$ from the above expression, we get
$\Rightarrow wv\left( \left( 3{{w}^{1}}{{v}^{5}} \right)-\left( 6{{w}^{2}} \right)+\left( 9{{w}^{2}} \right)+\left( 2{{w}^{2}} \right)-\left( 9{{w}^{1}}{{v}^{5}} \right) \right)$
Now, on further simplifying the above expression, we get
$\Rightarrow wv\left( 3{{w}^{1}}{{v}^{5}}-6{{w}^{2}}+9{{w}^{2}}+2{{w}^{2}}-9{{w}^{1}}{{v}^{5}} \right)$
Now, we see that we have three ${{w}^{2}}$ terms in the above expression, thus on solving we get
$\Rightarrow wv\left( 3{{w}^{1}}{{v}^{5}}+5{{w}^{2}}-9{{w}^{1}}{{v}^{5}} \right)$
Also, we see that we have two ${{w}^{1}}{{v}^{5}}$ terms in the above expression, therefore, on solving these terms, we get
$\Rightarrow wv\left( -6{{w}^{1}}{{v}^{5}}+5{{w}^{2}} \right)$
Now, we will use the distributive property $a(b-c)=ab-ac$ in the above expression, we get
$\Rightarrow -6{{w}^{2}}{{v}^{6}}+5{{w}^{3}}{{v}^{1}}$
Therefore, for the algebraic expression $3{{w}^{2}}{{v}^{6}}-6{{w}^{3}}v+9{{w}^{3}}v+2{{w}^{3}}v-9{{w}^{2}}{{v}^{6}}$ , its simplified value is equal to $-6{{w}^{2}}{{v}^{6}}+5{{w}^{3}}{{v}^{1}}$ .

Note:
While solving this problem, do mention the formulas you are using to avoid confusion and mathematical errors. One of the alternative methods to solve this problem is you can directly use the mathematical rules by adding or subtracting the like terms in the given expression, to get the accurate answer to the problem.