Let's substitute a=-1 and b=1 into the given expression:
(-1)^3 + 8(1)^3 - ((-1) + 2(1))((-1)^2 + 4(-1)(1) + 4(1))
= -1 + 8 - ((-1) + 2)(1 + 4(-1) + 4)
= -1 + 8 - (1 + 2)(1 - 4 + 4)
= -1 + 8 - 3(1 + 1)
= -1 + 8 - 3(2)
= -1 + 8 - 6
= 1
Therefore, the value of the expression A^3 + 8B^3 - (A + 2B)(A^2 + 4AB + 4B) when A=-1 and B=1 is 1.
Let's substitute a=-1 and b=1 into the given expression:
(-1)^3 + 8(1)^3 - ((-1) + 2(1))((-1)^2 + 4(-1)(1) + 4(1))
= -1 + 8 - ((-1) + 2)(1 + 4(-1) + 4)
= -1 + 8 - (1 + 2)(1 - 4 + 4)
= -1 + 8 - 3(1 + 1)
= -1 + 8 - 3(2)
= -1 + 8 - 6
= 1
Therefore, the value of the expression A^3 + 8B^3 - (A + 2B)(A^2 + 4AB + 4B) when A=-1 and B=1 is 1.