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 - 5= a^2 - a - 56
Right Side(a+10)(a-11= a^2 - 11a + 10a - 11= a^2 - a - 110
Now, we compare the two sides of the inequalitya^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).
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 - 5
= a^2 - a - 56
Right Side
(a+10)(a-11
= a^2 - 11a + 10a - 11
= 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).