(p + 2)^2 - (p + 11)^2

To simplify the expression, let's expand the squares.

Expanding the first square, (p + 2)^2:
(p + 2)(p + 2) = p(p) + p(2) + 2(p) + 2(2)
= p^2 + 2p + 2p + 4
= p^2 + 4p + 4

Expanding the second square, (p + 11)^2:
(p + 11)(p + 11) = p(p) + p(11) + 11(p) + 11(11)
= p^2 + 11p + 11p + 121
= p^2 + 22p + 121

Now, substitute the expanded squares back into the expression:
(p + 2)^2 - (p + 11)^2 = (p^2 + 4p + 4) - (p^2 + 22p + 121)

Next, remove the parentheses:
= p^2 + 4p + 4 - p^2 - 22p - 121

Combining like terms:
= (p^2 - p^2) + (4p - 22p) + (4 - 121)
= -18p - 117

So, the simplified expression is -18p - 117.