Expand and simplify :

(x+6)^2
(b+9)(b-9)

To expand and simplify expressions, you need to apply the distributive property and combine like terms.

1. Expanding and simplifying (x+6)^2:
To expand this expression, we need to multiply each term in the expression by itself and then combine like terms.

(x+6)^2 = (x+6)(x+6)

First, we apply the distributive property to the first term in the second set of parentheses:
(x+6) * x = x^2

Next, we apply the distributive property to the second term in the second set of parentheses:
(x+6) * 6 = 6x + 36

Now, we apply the distributive property to the first term in the first set of parentheses:
x * (x+6) = x^2 + 6x

Finally, we apply the distributive property to the second term in the first set of parentheses:
6 * (x+6) = 6x + 36

Now, we can combine the like terms:
x^2 + 6x + 6x + 36 = x^2 + 12x + 36

Therefore, (x+6)^2 simplifies to x^2 + 12x + 36.

2. Expanding and simplifying (b+9)(b-9):
To expand this expression, we again use the distributive property:

(b+9)(b-9) = b(b-9) + 9(b-9)

First, we apply the distributive property to the first term in the first set of parentheses:
(b) * (b-9) = b^2 - 9b

Next, we apply the distributive property to the second term in the second set of parentheses:
9 * (b-9) = 9b - 81

Now, we can combine the like terms:
b^2 - 9b + 9b - 81

The -9b and +9b terms cancel each other out, leaving us with:
b^2 - 81

Therefore, (b+9)(b-9) simplifies to b^2 - 81.