a^3 + a^2c + abc + b^2c - b^3

= a(a^2 + ac + bc) + b(b^2 - c)

= a(a(c + a) + bc) + b(b^2 - c)

= a^2(c + a) + abc + b(b^2 - c)

= a^2c + a^3 + abc + b(b^2 - c)

= a^2c + a^3 + abc + b(b - c)(b + c)

= a^2c + a^3 + abc + b(b - c)(b + c)

= a^2c + a^3 + abc + b(b - c)(b + c)