## Expanding (5n + 2)^2

The expression (5n + 2)^2 represents the square of a binomial. To expand it, we can use the **FOIL** method (First, Outer, Inner, Last) or the **square of a binomial pattern**.

### Using the FOIL Method:

**First:**Multiply the first terms of each binomial: (5n) * (5n) =**25n^2****Outer:**Multiply the outer terms: (5n) * (2) =**10n****Inner:**Multiply the inner terms: (2) * (5n) =**10n****Last:**Multiply the last terms: (2) * (2) =**4**

Now, combine the terms: 25n^2 + 10n + 10n + 4

Finally, simplify by combining the middle terms: **25n^2 + 20n + 4**

### Using the Square of a Binomial Pattern:

The square of a binomial pattern states: (a + b)^2 = a^2 + 2ab + b^2

In our case, a = 5n and b = 2. Applying the pattern:

(5n + 2)^2 = (5n)^2 + 2(5n)(2) + 2^2

Simplifying: **25n^2 + 20n + 4**

### Conclusion

Both methods result in the same expanded expression: **25n^2 + 20n + 4**.

This expression represents a **quadratic trinomial** with a leading coefficient of 25, a linear coefficient of 20, and a constant term of 4. It can be used in various algebraic manipulations and problem-solving scenarios.