## Expanding the Expression (6x + 7)²

The expression (6x + 7)² represents the square of a binomial. To expand it, we can use the **FOIL method** or the **square of a binomial formula**.

### Using the FOIL Method

FOIL stands for **First, Outer, Inner, Last**. This method helps us multiply each term in the first binomial with each term in the second binomial:

**First:**Multiply the first terms of each binomial: (6x)(6x) = 36x²**Outer:**Multiply the outer terms of the binomials: (6x)(7) = 42x**Inner:**Multiply the inner terms of the binomials: (7)(6x) = 42x**Last:**Multiply the last terms of each binomial: (7)(7) = 49

Now, combine the terms: 36x² + 42x + 42x + 49

Simplify the expression by combining like terms: **36x² + 84x + 49**

### Using the Square of a Binomial Formula

The square of a binomial formula states: (a + b)² = a² + 2ab + b²

In our case, a = 6x and b = 7. Applying the formula:

(6x + 7)² = (6x)² + 2(6x)(7) + 7²

Simplifying the expression: **36x² + 84x + 49**

### Conclusion

Both the FOIL method and the square of a binomial formula lead to the same expanded expression: **36x² + 84x + 49**.

This expanded form is a **quadratic trinomial** with a leading coefficient of 36, a linear coefficient of 84, and a constant term of 49.