1) (x+1)(x^2-x+1) = xx^2 - xx + x + x^2 - x + 1 = x^3 - x^2 + x + x^2 - x + 1 = x^3 + 1
2) (a-c)(a^2+ac+c^2) = aa^2 + aac + ac^2 - ca^2 - cac - cc^2 = a^3 + a^2c + ac^2 - a^2c - ac^2 - c^3 = a^3 - c^3
1) (x+1)(x^2-x+1)
= xx^2 - xx + x + x^2 - x + 1
= x^3 - x^2 + x + x^2 - x + 1
= x^3 + 1
2) (a-c)(a^2+ac+c^2)
= aa^2 + aac + ac^2 - ca^2 - cac - cc^2
= a^3 + a^2c + ac^2 - a^2c - ac^2 - c^3
= a^3 - c^3