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The problem is to factor the given polynomial:

\[
10x(x + y) + 3(x + y)
\]

### Solution:

1. Notice that both terms have a common factor \((x + y)\).
2. Factor out \((x + y)\) from the expression:

   \[
   10x(x + y) + 3(x + y) = (x + y)(10x + 3)
   \]

Therefore, the factored form of the polynomial is:

\[
\boxed{(x + y)(10x + 3)}
\]

Would you like further details, or do you have any questions?

### Related Questions:
1. How do you identify the greatest common factor in an expression?
2. What are the steps for factoring polynomials with multiple terms?
3. How do you factor expressions that involve variables and coefficients?
4. Can the expression \((10x + 3)\) be factored further?
5. How does factoring simplify solving polynomial equations?

**Tip:** Always look for a common factor in all terms when factoring expressions!

Factor the given polynomial: 10x(x + y) + 3(x + y)

Learn how to factor the polynomial 10x(x + y) + 3(x + y) by using the distributive property. This solution covers essential algebraic concepts related to factoring and simplifying polynomials. Suitable for students in Grades 8-10.

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