(a+2)(2^2-2a+4) = a(2^2) + a(-2a) + a(4) + 2(2^2) + 2(-2a) + 2(4)= 4a - 2a^2 + 4 + 8 - 4a + 8= -2a^2 + 12
(x+1)(x^2-x+1) = x(x^2) + x(-x) + x(1) + 1(x^2) + 1(-x) + 1= x^3 - x^2 + x + x^2 - x + 1= x^3 + 1
(a+2)(2^2-2a+4) = a(2^2) + a(-2a) + a(4) + 2(2^2) + 2(-2a) + 2(4)
= 4a - 2a^2 + 4 + 8 - 4a + 8
= -2a^2 + 12
(x+1)(x^2-x+1) = x(x^2) + x(-x) + x(1) + 1(x^2) + 1(-x) + 1
= x^3 - x^2 + x + x^2 - x + 1
= x^3 + 1