## Expanding (5a + 2)^2

The expression (5a + 2)^2 represents the square of the binomial (5a + 2). To expand this expression, we can use the **FOIL method** or the **square of a binomial formula**.

### Expanding using FOIL method:

**FOIL** stands for **First, Outer, Inner, Last**. This method helps us multiply two binomials.

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

Now, add all the results together:

25a^2 + 10a + 10a + 4 = **25a^2 + 20a + 4**

### Expanding using Square of a Binomial Formula:

The formula for the square of a binomial is: **(a + b)^2 = a^2 + 2ab + b^2**

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

(5a + 2)^2 = (5a)^2 + 2(5a)(2) + (2)^2

Simplifying:

(5a + 2)^2 = **25a^2 + 20a + 4**

### Conclusion:

We can see that both methods lead to the same result: **(5a + 2)^2 = 25a^2 + 20a + 4**.

Remember, choosing which method to use depends on your personal preference and comfort level. Both methods are valid and effective for expanding the square of a binomial.