5x²+10xy+5y

It looks like you have a mathematical expression, specifically a polynomial: \( 5x^2 + 10xy + 5y \).

To simplify or factor this expression, we can look for common factors in each term:

1. Identify Common Factors: In each term of the expression, \( 5 \) is a common factor.

2. Factor out the common term:

   \[ 5x^2 + 10xy + 5y = 5(x^2 + 2xy + y) \]

Now, we can try to factor the quadratic part \( x^2 + 2xy + y \) further.

We can see if this quadratic can be factored into a product of two binomials:

• The expression \( x^2 + 2xy + y \) doesn't factor nicely into integer pairs, and is thus left in its current form.

So, the final factored expression is:

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

If you are looking for a specific kind of manipulation or simplification, let me know!