Tutor profile: Apoorva S.
What is the subjunctive? How do I conjugate it? What is its equivalent in the English language?
The subjunctive is not a tense of the French language, instead, it's better to conceptualize it as a mood. It is used in specific situations and sometimes it will be "triggered" by certain sentence structures. The acronym WEIRDO is often used to describe situations in which you *must* use the subjunctive. W = Wish, E = emotion, I = impersonal expressions, R = requirements, D = doubt, O = other phrases. The subjunctive is often triggered (déclenché) by what's in the first clause i.e. "I am happy you are here." Here, the second clause (or second half of the sentence) must be in the subjunctive in French. As you may notice, we are simply using the present tense in English ("are"), so it's challenging to come up with an accurate equivalent in English. I'd be happy to discuss language change and historical linguistics with you if that interests you, but in interest of staying relevant, we would conjugate "are" in the subjunctive in French since we expressed the E (emotion) in the first clause (I am happy...). The translation would look like so: "Je suis heureu(x/se) que vous/tu soyez/sois ici." The conjugation of the subjunctive (in my opinion) is pretty formulaic except for the verbs that behave exceptionally -- would it be French if we didn't have exceptions? Typically, we want to take the root of the 3rd plural (ils/elles) and drop the "-ent" -- that's our root. We then want to add these endings: Je -e, Tu -es, Il/Elle -e, Nous -ions, Vous -iez, Ils/Elles -ent. There are exceptions to this rule as you may note from the verb être above conjugated as "soyez/sois." I'd be happy to walk you through the rules more. They are really fun to learn!
How can I write a streamlined yet detailed essay?
In order to write an essay, depending on the field, you may consider starting with a literature review. Sometimes you might know exactly what you want to write about but if you're like me, you might be deciding still which is why a literature review is a great place to start. Most fields such as psychology and business prefer newer research articles because conventions and practices are constantly evolving and changing. However, be cautious to not simply discard older research articles because key theory papers from the 1960's still remain relevant and applicable. After conducting a thorough literature review, it's important to ask yourself this: how many of these articles will actually strengthen the points I am making? One of the issues I see consistently in research articles is this -- people cite for the sake of citing. Remember, a shorter, succinct, and cohesive references/works cites goes way further than a clunky, long list that may not as pertinent to your topic. It's best to save editing till the midway point or the end. Getting caught up in editing may slow your writing roll down and it might be best to first get words on paper before you go in with your editing hat on. It's crucial to let some of the pressure off and get words onto the document without constantly editing what you write. It's normal to get stuck or feel exhausted, take a break, a walk, have a cup of tea and come back to it. Writing can be extremely therapeutic and relaxing once you find your ritual. I am of the belief that reading is breathing in and writing is breathing out; they go hand in hand.
How do you unpack an algebraic expression which is in complex parentheses? for e.g. $$(x+y)^2$$ and $$(x-y)^2$$?
A: These are the fundamental algebraic expressions that you may want to memorize. However, it is important to understand the logic of the expression before we attempt to remember it. The first expression cannot simply be unpacked as $$x^2+y^2$$, that would be wrong. When the sum of x and y are squared, the output will have three elements. Therefore, the expression $$(x+y)^2$$ can rather be visualized as $$(x+y) (x+y)$$. We have to use FOIL which stands for First Outside Inside Last to unpack this. By the virtue of FOIL, we would distribute the x from the first parenthesis to the second parenthesis like so -> $$x(x+y)$$. Then we will distribute the $$+y$$ of the first brackets to the second parenthesis, like so -> $$+y(x+y)$$. The first parenthesis unfolds like this: $$x(x+y)$$ = $$x^2+xy$$. The second parenthesis looks like this: $$+y(x+y)$$ = $$y^2+xy$$. Now when we combine this we get: $$x^2+xy+y^2+xy$$. Combining the like terms, we get $$x^2+2xy+y^2$$. The same logic applies to the expression $$(x-y)^2$$.
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