The end of the verse mentioned above mentions purification twice. The first mention of this word means "to purify you" and the second mention according to Arabic grammar relates to the "type" of purification.
What is that specific type of purification? Some translations have translated it as extensive purification or other types of purification. Please mention evidences or hadith to show what type of purification Allah means in this verse
وَقَرْنَ فِي بُيُوتِكُنَّ وَلَا تَبَرَّجْنَ تَبَرُّجَ الْجَاهِلِيَّةِ الْأُولَى وَأَقِمْنَ الصَّلَاةَ وَآتِينَ الزَّكَاةَ وَأَطِعْنَ اللَّـهَ وَرَسُولَهُ إِنَّمَا يُرِيدُ اللَّـهُ لِيُذْهِبَ عَنكُمُ الرِّجْسَ أَهْلَ الْبَيْتِ وَيُطَهِّرَكُمْ تَطْهِيرًا
And abide in your houses and do not display yourselves as [was] the display of the former times of ignorance. And establish prayer and give zakah and obey Allah and His Messenger. Allah intends only to remove from you the impurity [of sin], O people of the [Prophet's] household, and to purify you with [extensive] purification. http://tanzil.net/#33:33
Please note the evidence or proof for type of purification is needed and not only the personal idea of an interpreter even if he is a famous interpreter.