## Simplifying (4x + 5)^2

The expression (4x + 5)^2 represents the square of the binomial (4x + 5). To simplify this, we can use the **FOIL method** or the **square of a binomial pattern**.

### Using the FOIL Method

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

**First:**Multiply the first terms of each binomial: (4x) * (4x) = 16x^2**Outer:**Multiply the outer terms of the binomials: (4x) * (5) = 20x**Inner:**Multiply the inner terms of the binomials: (5) * (4x) = 20x**Last:**Multiply the last terms of each binomial: (5) * (5) = 25

Now, combine the terms: 16x^2 + 20x + 20x + 25

Finally, simplify by combining like terms: **16x^2 + 40x + 25**

### 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 = 4x and b = 5. Applying the pattern:

(4x + 5)^2 = (4x)^2 + 2(4x)(5) + (5)^2

Simplifying: **16x^2 + 40x + 25**

### Conclusion

Both methods lead to the same simplified expression: **16x^2 + 40x + 25**. Remember, when dealing with squared binomials, using the appropriate pattern can save you time and effort.