Dtzach Adash B'Achav - The Secret Behind The Words
The Hagada tells us that Rebbi Yehuda made and mnemonic to remember the 10 makos. Was that all this is about? Is there any significance in the words themselves? The Otzar Divrei HaMeforshim brings a number of explanations for these words.
The Chavas Da'as explains that while we are happy to see the downfall of our oppressors the Mitzrim, since we are in Galus we need to be quiet about our happiness. Dtzach is from Ditza, happiness. Adash is a lentil which is silent and has no opening or mouth as Chazal tell us. Dtzach Adash, our happiness at the seder should be done quietly so as not to make waves in Galus. For this reason we therefore also perform signs of aveilus at the seder like eating an egg. B'Achav, or B'Ahava means that we will continue to struggle in our galus with love for Hashem as we wait for the day of our final geula, when our happiness will be complete and out in the open.
The Hagadah Marbeh L'Saper from the son of the Korban Nesanel says that as part of Yaakov's purchase of he Bechor from Eisav, we had to suffer slavery in Mitzrayim. The entire time Bnei Yisroel were in Mitzrayim they were unhappy with the deal that Yaakov made. Only after they went out, were they happy. Dtzach - only now were they happy. Adash - with the sale of the Bechor for Adashim. B'Achav - that Yaakov purchased from his brother.
The Nefesh Yehonoson says that the mishna in Brachos says we must give a bracha to Hashem for the bad just like we do for the good. Dtzach, in time of happiness, Adash, in times of aveilus when we eat lentils, B'Achav, we accept them both from Hashem with love.