First expression:
(a-4)(a^2+4a+16)
Expand using the distributive property:
a(a^2) + a(4a) + a(16) - 4(a^2) - 4(4a) - 4(16)
a^3 + 4a^2 + 16a - 4a^2 - 16a - 64
Combine like terms:
a^3

Second expression:
121-(-8)^2
First calculate the square of -8:
(-8)^2 = (-8)(-8) = 64
Now substitute the value back into the original expression:
121-64
Perform the subtraction:
121-64 = 57

Therefore, the final expression is:
a^3 + 57