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