Commentaire sur L’Exode 8:1

אמור אל אהרן נטה את מטך, “say to Aaron to stretch out his staff, etc.” seeing that we have been told earlier (6,6) that G’d would employ His זרוע נטויה, “outstretched arm,” when the “hand” was employed instead, the Torah had to spell this out. Ibn Ezra claims that the stretching out of Aaron’s hand with the staff in all four directions resulted in the frogs emerging from the streams and rivers as well as from the lakes, but not from the ponds.

נטה את ידך, “extend your hand!” G-d wanted Pharaoh and the Egyptians to see that the cause of the plague wasMoses, although it was Aaron who actually extended his arm with Moses’ staff over the river.8.2. ותעל הצפרדע, “the frogs emerged from the river.” Even though the Torah uses the singular mode here, the meaning is that swarms of frogs came forth. We find something similar in Numbers 21,7 when the Torah describes the plague of snakes besetting the people as if it had been only a single snake, i.e. ויסר מעלינו את הנחש, “may He remove the snake(s) from us.”