Why does the Torah write "ha'Tzefarde'a" in the singular?
Rashi #1 (citing the Tanchuma): Because only one frog emerged from the river at first. When the Egyptians began striking it, hordes of frogs began to swarm from it - the more they hit it, the more frogs emerged - until the whole of Egypt was full of frogs. 1
Rashi #2: According to the simple explanation, the Torah tends to refer to a swarm in the singular. 2
Why did Hashem initially send only one frog?
Oznayim la'Torah: To give the Egyptians a chance to relent. 1
See Oznayim la'Torah. Had they done so, the frog would have disappeared. Only they opted to 'put out the fire with oil' - They began beating it, causing more and more to frogs to emanate from it, until they spread out over the whole of Egypt.
QUESTIONS ON RASHI
Rashi writes: "'Va'Ta'al ha'Tzefarde'a' - It was [at first just] one frog." If we may interpret this way, why not do so for the singular word "ha'Kinam" (8:13,14) as well?
Maharal (Gevuros Hashem, beg. Ch. 33, p. 124): It is normal for Kinim (lice) to assemble as a group --to which we may refer in the singular, 'Kinam.' Frogs usually do not group; and so the singular "Tzefarde'a" needs interpretation.
Rashi writes: "'Va'Ta'al ha'Tzefarde'a' - At first, just one frog [emerged from the river]; the Mitzrim hit it, and it spewed forth many swarms [of frogs]." Another opinion in the Gemara (Sanhedrin 67b) is that the frog whistled, and all the others followed. What is behind this Machlokes?
Maharal (Gevuros Hashem, beg. Ch. 33, p. 124): Why does the Torah refer to the numerous frogs as "Tzefarde'a," in the singular? To the first opinion (R' Akiva), it is because one frog produced all of them. The second opinion (R' Elazar b. Azaryah) is that they are called one due to the one frog that gathered them all.
Rashi writes: "'Va'Ta'al ha'Tzefarde'a' - At first, just one frog [emerged from the river]...." If so, how do we explain the verse above, "The river shall teem forth frogs "(7:28)?
Maharal: Refer to 7:28:1.1:1.