(p-7)(p+8)

To simplify the expression (p-7)(p+8), you can use the distributive property. The distributive property states that when you multiply a sum by another number, you can multiply each term inside the sum separately and then add the results. In this case, you need to multiply each term of the first factor, p-7, by each term of the second factor, p+8.

Using the distributive property:

(p-7)(p+8) = p(p+8) - 7(p+8)

Now, let's simplify each part:

p(p+8) = p^2 + 8p
-7(p+8) = -7p - 56

Now, let's put the simplified parts together:

(p-7)(p+8) = p^2 + 8p - 7p - 56

Finally, simplify the terms:

p^2 + 8p - 7p - 56 = p^2 + p - 56

So, the simplified expression for (p-7)(p+8) is p^2 + p - 56.