Answer
The required value is $\left( y-5 \right)\left( {{y}^{2}}+5y+25 \right)$.
Work Step by Step
Consider the expression,
${{y}^{3}}-125$
Evaluate the given expression:
${{y}^{3}}-125={{\left( y \right)}^{3}}-{{\left( 5 \right)}^{3}}$
Use the formula as follows:
${{A}^{3}}-{{B}^{3}}=\left( A-B \right)\left( {{A}^{2}}+AB+{{B}^{2}} \right)$
Then, the expression is:
$\begin{align}
& {{y}^{3}}-125=\left( y-5 \right)\left( {{\left( y \right)}^{2}}+\left( y \right)\left( 5 \right)+{{\left( 5 \right)}^{2}} \right) \\
& =\left( y-5 \right)\left( {{y}^{2}}+5y+25 \right)
\end{align}$
Therefore, the value of ${{y}^{3}}-125$ is $\left( y-5 \right)\left( {{y}^{2}}+5y+25 \right)$.
