All you can factor out is the common factor 2. 2(a^3 - 64)
2a3-16a2+30a Factor out 2a: 2a(a2-8a+15) (2a)(a-5)(a-3) This is the most factored form of this expression.
Since you know the values of the two variables, a and y, plug it into the expression like this: 2a3 - 3ay = 6a - 3ay = 6(-1) -3(-1)(2) = -6 -3(-2) =-6 + 6 = 0
(a - 1)(a - 1)(a^2 + a + 1)(a ^2 + a + 1)
In rationalising quadratics 2a3 - 5a2 - 39 is an irrelevance. It is not a quadratic but a cubic and so not within the defined scope.
(2a3)(10a5)/4a1
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Solve the following equation for A : 2A/3 = 8 + 4A
If by "2aXaXa", you actually mean "2a3", then the derivative with respect to a is 6a2. On the other hand, if you actually mean "2a3X2", then it's derivative with respect to X would be 6a2X2(da/dx) + 4a3X. If "a" is simply a constant though, then it's derivative is 4a3X
For every 2 moles of A3, 3 moles of B2 react to form 6 moles of AB. Since we have 10 moles of A3, we need to double the moles of B2 reacting, which would be 15 moles of B2 to fully react with the 10 moles of A3. This would produce 30 moles of AB.
From the balanced equation, 2 moles of A3 react with 3 moles of B2 to produce 6 moles of AB. Therefore, if 10 moles of A3 are reacted, the ratio of moles of AB produced would be (10 moles A3 / 2 moles A3) * 6 moles AB = 30 moles AB.
Team DuelingBasic RulesThe match is between two teams; of two players each (designated player A and player B).Teammates are seated next to each other with the other team on the opposite side of the table.For a tournament, each player's designation (A or B) is chosen at the start of the tournamentand never changes.Each player has 5 Monster Card Zones.Each player has 5 Spell & Trap Card Zones.The zones from both players on a team create 1 large side of the field. So there are 2 sides ofthe field, Team One's side of the field and Team Two's side of the field.Each player uses their own Deck (2 Decks per team).Each player has their own Graveyard (you cannot use your teammate's Graveyard as if it wasyour own).Each team has 1 Life Point total of 8000 (if it reaches zero, the team loses).There can only be 1 Field Spell Card in play at a time, just like a 1-on-1 Duel.Each player has their own Fusion Deck (you cannot use your teammate's Fusion Deck for yourFusion Summons or card effects).Each player has their own Side Deck to use only with their Deck.Limited Cards are counted per player, not per team. So, for any given Limited Card, each playeron a team could include 1 copy in their Deck, making a total of 2 copies that team can use.However, one player cannot include 2 copies of a Limited Card, even if the other player doesn'tinclude any.© 1996 KAZUKI TAKAHASHI© 2 0 0 4 N A S T V T O K Y OTeammates may talk, compare hands, and share information freely with each other. Teammatesmust come to an agreement before making plays involving each other's cards. They shouldmake their decisions in a timely manner as to not delay the game.A team loses if either player on that team cannot draw a card from their Deck when required to.Turn ProcedurePlayers on the same team sit next to each other, player A sits to the right of player B. Team 1 isplayers 1A & 1B and Team 2 is players 2A & 2B. The turn order starts with player A of the teamthat is chosen to go first and then alternates between teams.The first player who can make an attack is the player who goes fourth. (In the example below,player 2B.)Turnthe Turn Player----------------------------------------------------1: Team 1Player 1A2: Team 2Player 2A3: Team 1Player 1B4: Team 2Player 2B5: Team 1Player 1AContinue until one team wins.© 1996 KAZUKI TAKAHASHI© 2 0 0 4 N A S T V T O K Y O© 1996 KAZUKI TAKAHASHI© 2 0 0 4 N A S T V T O K Y OCard EffectsIf any part of a card affects your opponent's hand, Deck, Fusion Deck, Graveyard, or RemovedZone, then the player activating the card effect must choose 1 of their opponents to apply theentire effect of the card to.EXAMPLES: "Confiscation," "Memory Crusher," "Soul Release," "Secret Barrel," "CrushCard Virus."If a card affects only your opponent's side of the field, it affects the entire side, or both youropponents.EXAMPLE: Player 2A activates "Lightning Vortex." It destroys player 1A and player 1B'sface-up monsters.If a card affects "both players," all 4 players are affected.EXAMPLE: "Dark World Dealings" is activated. All 4 players will each draw a card, then eachdiscard a card.If a card references another card that "you control," it counts cards in your teammate's Zones aswell as your own. In the same way, cards that reference a card "your opponent controls" countboth opponent's sides of the field.EXAMPLE: Player 1A has "The Six Samurai ­ Zanji" on the field and Player 1B has "The SixSamurai ­ Irou" on the field. Player 1A can Special Summon "Great Shogun Shien" from hishand because his team controls 2 or more "Six Samurai" monsters.A player can allow their teammate to use monsters in their Monster Card Zones as Tributes,Fusion Materials, or for other appropriate card effects.EXAMPLE: It is player 1A's turn, and player 1B controls a "Gravekeeper's Spy." Withpermission, player 1A Tributes that "Gravekeeper's Spy" to Tribute Summon his "Jinzo."Cards Set by a player can be viewed by the teammate, but they must be activated by the playerwho Set them."Owner" means the same thing as a standard Duel. The "owner" is the player who's Deck thecard started in.© 1996 KAZUKI TAKAHASHI© 2 0 0 4 N A S T V T O K Y OAttackingYou can only attack with monsters you control (in your 5 zones) during your turn. You cannotattack with your teammate's Attack Position monsters.If there is a monster on the opponents' side of the field (in either player's Monster Card Zones)then you must attack it before attacking their Life Points directly.EXAMPLE: Player A has "Elemental Hero Sparkman" in Attack Position. Player C has nomonsters, but Player D has "Dark Magician" in Attack Position. Player A cannot attack directly,because the opponents have "Dark Magician" on the field.Additional RulesDuring a player's turn, either opponent may activate Spell Speed 2 or higher effects (just asthey could in a standard Duel). The teammate may also activate Spell Speed 2 or higher effects(as if it was an opponent's turn).When a player activates an effect, each other player must be given the opportunity to add aneffect to the chain before it is resolved (starting with an opponent and then alternating betweenteams).If multiple trigger effects activate at the same time, the turn player's effects will be added to thechain first, followed by their teammate's effects, and finally the opponents' effects (in an orderof their choosing).Card effects that count turns count all appropriate turns.EXAMPLE: "Swords of Revealing Light" is activated by Player A of Team 1. Team 2 cannotattack on Player C's next turn (1 turn), Player D's next turn (2 turns), and Player C's turn afterthat (3 turns). "Swords of Revealing Light" will be destroyed at the end of that turn, becausethree opponents' turns have passed.