How to explain the process of deriving a mathematical expression?

We obtain a formula after some mathematical manipulations as: y=5+log(sin(a)).

Now I want to explain how we can obtain another formula based on what we already derived. Compare:

1. It only requires a to be substituted by a+b.

2. We only need to set a to a+b.

I think the first sentence is focused on replacement; It says we can reach to a certain formula through replacing something with something else. (I prefer this sentence)

However, the second sentence implying a variable that can take multiple values and we set the variable to the of interest value, a+b. (I don't prefer this sentence)

Questions:

Q1: Is it correct to use passive form of the infinitive as what I've used in #1?

Q2: Is there any situation in which we must choose only one of them?

Q3: How can I explain such processes correctly? (Are there better sentences?)

Thanks.

• In your Q1, where does the wording "passive form of the infinitive" come from? I suppose you call "to set" "passive", but why? Oct 24 '15 at 23:49
• @VictorBazarov It was typo,my intent was "to be substituted". Oct 25 '15 at 7:55

The second sentence is first person, which is unusual. In the first sentence, you are using the pronoun "It" but we don't ever learn what you are referring to, so context is missing. Also, 'only requires' could be misinterpreted and appears misplaced somehow.

Contrary to what others might say, I believe it is better to use direct action verbs. The following is a better sentence for 1):

The second formula is obtained by simply substituting a with a+b.

The following is a better sentence for 2):

We can derive the second formula just by setting a to a+b in the first formula.

• Regarding active vs. passive voice - You are correct that passive is not always the correct choice. An question on Academia.SE has generated a good discussion on the relative merits & acceptability of each. See academia.stackexchange.com/questions/12400/… See the
Mar 30 '16 at 17:42

Q1. Your sentence (1) should be "It only requires that A be substituted by A+B" Q2, Q3. Not really, but in a formal derivation I would not use 'only' , and would write something more like:

Substituting A+B for A yields {the new formula) ...

While skipping 20 minutes of the explanation use "It is intuitively obvious to the casual observer that ..."

More seriously ...

If I were writing I'd use 1.

Scientific style writing mostly leaves out personal pronouns unless the discussion is some sort of biography or history.

If I was lecturing to a group I'd use 2.

I'd want the listeners to feel like we're having a personal discussion, not that I am droning from a pulpit.