5x²+10xy+5y²

The expression you have provided is \(5x^2 + 10xy + 5y^2\). This expression can be factored.

First, notice that each term has a common factor of \(5\). Factoring out \(5\), we get:

\[ 5(x^2 + 2xy + y^2) \]

Next, we can factor the quadratic expression \(x^2 + 2xy + y^2\). This expression is a perfect square trinomial, and it can be factored as:

\[ (x + y)^2 \]

Thus, putting it all together, the complete factored form of the original expression is:

\[ 5(x + y)^2 \]

So, the final answer is:

\[ 5(x+y)^2 \]