The expression given is:

\[
5x + 50 + xy + 10y
\]

This is a polynomial with two variables, \(x\) and \(y\). Let's analyze the expression step-by-step:

1. **Grouping Like Terms**: We can group the terms by their variable factors to make it easier to understand:
   \[
   (5x + xy) + (50 + 10y)
   \]

2. **Simplification**: No like terms can be combined further (since there are no terms with the same variables or constants).

The expression is already in its simplest form. If you wanted to factor it partially or look for common factors, you could rewrite parts of it like this:

- From the first group, \(5x + xy = x(5 + y)\).
- From the second group, \(50 + 10y = 10(5 + y)\).

So the entire expression can be factored as:

\[
5x + 50 + xy + 10y = x(5 + y) + 10(5 + y)
\]

Now, notice that \((5 + y)\) is a common factor:

\[
= (5 + y)(x + 10)
\]

### Final Factored Form

The expression in its factored form is:

\[
(5 + y)(x + 10)
\]

### Would you like further details or explanations?

Here are 5 related questions that build on this information:

1. How do you find the greatest common factor of terms in a polynomial?
2. What is the difference between a monomial, binomial, and polynomial?
3. How do you expand a factored expression back into its original form?
4. Can you explain how to factor polynomials with more than two variables?
5. How does factoring help solve polynomial equations?

**Tip:** When factoring expressions, always look for the greatest common factor first; it simplifies the process and reduces the chance of errors.

Learn how to factor the polynomial expression 5x + 50 + xy + 10y using algebraic methods. This solution demonstrates the process of grouping terms, identifying common factors, and applying the distributive property. Suitable for students in Grades 9-11.

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