To prove this inequality, we will expand both sides of the inequality and simplify the expression:

Left Side:
(a-8)(a+7)
= a^2 + 7a - 8a - 56
= a^2 - a - 56

Right Side:
(a+10)(a-11)
= a^2 - 11a + 10a - 110
= a^2 - a - 110

Now, we compare the two sides of the inequality:
a^2 - a - 56 > a^2 - a - 110

Subtracting a^2 and -a from both sides, we get:
-56 > -110

This inequality holds true since -56 is greater than -110.

Therefore, we have proven that (a-8)(a+7) > (a+10)(a-11).