Answer
The required value is $\left( x+5+3y \right)\left( x+5-3y \right)$.
Work Step by Step
Consider the expression,
${{x}^{2}}+10x+25-9{{y}^{2}}$
Now, evaluate the given expression:
${{x}^{2}}+10x+25-9{{y}^{2}}={{\left( x \right)}^{2}}+2\left( 5 \right)\left( x \right)+{{\left( 5 \right)}^{2}}-9{{y}^{2}}$
Use the formula as follows:
${{A}^{2}}+2AB+{{B}^{2}}={{\left( A+B \right)}^{2}}$
Then, the expression becomes:
$\begin{align}
& {{x}^{2}}+10x+25-9{{y}^{2}}={{\left( x+5 \right)}^{2}}-9{{y}^{2}} \\
& ={{\left( x+5 \right)}^{2}}-{{\left( 3y \right)}^{2}}
\end{align}$
Again, use the following formula:
${{A}^{2}}-{{B}^{2}}=\left( A+B \right)\left( A-B \right)$
Then, the expression is:
${{x}^{2}}+10x+25-9{{y}^{2}}=\left( x+5+3y \right)\left( x+5-3y \right)$
Therefore, the value of ${{x}^{2}}+10x+25-9{{y}^{2}}$ is $\left( x+5+3y \right)\left( x+5-3y \right)$.
