If a spell you cast has {X} in its mana cost, you choose the value of X before calculating the spell’s total cost. For example, if a spell’s mana cost is {X}{R} and your opponents have drawn two cards this turn, you could choose 5 as the value of X and pay {3}{R} to cast the spell.

If there are additional costs to cast a spell, or if the cost to cast a spell is increased by an effect (such as the one created by Thalia, Guardian of Thraben’s ability), apply those increases before applying cost reductions.

That ability can’t reduce the amount of colored mana you pay for a spell. It reduces only the generic mana component of that cost.

The cost reduction can apply to alternative costs such as flashback costs.

The last ability of Heliod, the Warped Eclipse doesn’t change the mana cost or mana value of any spell. It changes only the total cost you pay.

The “as though they had flash” effect applies only to casting spells. It does not, for example, change when you may activate abilities that can be activated “only as a sorcery.”