'Explanative' and 'explanatory' are both adjectives, and 'increase' and 'increasing' are both nouns. Are the meanings of the words in each pair the same? If the meanings aren't the same, and the words in each pair aren't interchangeable, could you please give me the reason why not?
The first pair, 'explanative' and 'explanatory' have the same meaning, although 'explanative' is very seldom used and might not be easily understood by many speakers, at least in North America. I would recommend using only 'explanatory' in your speech.
The second pair 'increase' and 'increasing' also have the same meaning as nouns, but again, the second one, 'increasing', is almost never used as a noun. As a noun, 'increase' means a rise in the amount, number or value of something.
There was a huge increase in winners this year. It was even bigger than last year's increase.
If used in the same sentence, the word 'increasing' would be a nominalized verb and would likely be followed by a different preposition. The use of nominalized verbs is rapidly declining in common speech. While many nominalized verbs are still widely used, the use of 'increasing' as a noun sounds awkward and should be avoided.
There was a huge increasing of winners this year. It was even bigger than last year's increasing.
The word 'increasing' is most often used as a verb or adjective.
The amount of daylight is increasing every day.
The increasing difficulty of getting tickets discourages many fans.