In الْمَبْثُوثِ, bāʾ is sākin in «مَبْ». It is a qalqalah letter, so release it cleanly without inventing a vowel. This is internal, minor qalqalah.
The article lām before mīm is pronounced. The wāw in «ثُو» is a madd letter and gets natural length.
Keep the two rules separate:
مَبْ — bāʾ qalqalah.
ثُو — natural wāw madd.
In الْمَنْفُوشِ, a sākin nūn meets fāʾ, a letter of ikhfāʾ. Hide the nūn with an appropriate ghunnah; neither pronounce it fully nor merge it into fāʾ.
«فُو» has a natural wāw madd. Thus the word contains ikhfāʾ followed by natural madd.
Contrast:
الْمَنْفُوشِ — nūn sākin + fāʾ: ikhfāʾ.
الْعِهْنِ — the nūn is vowelled; no nūn-sākin rule applies there.
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Qalqalah and ikhfāʾ in two consecutive words
Al-Qāriʿah and Az-Zalzalah — Comparative Tajwīd Practice
In الْمَبْثُوثِ, bāʾ is sākin in «مَبْ». It is a qalqalah letter, so release it cleanly without inventing a vowel. This is internal, minor qalqalah.
The article lām before mīm is pronounced. The wāw in «ثُو» is a madd letter and gets natural length.
Keep the two rules separate:
مَبْ — bāʾ qalqalah.
ثُو — natural wāw madd.
In الْمَنْفُوشِ, a sākin nūn meets fāʾ, a letter of ikhfāʾ. Hide the nūn with an appropriate ghunnah; neither pronounce it fully nor merge it into fāʾ.
«فُو» has a natural wāw madd. Thus the word contains ikhfāʾ followed by natural madd.
Contrast:
الْمَنْفُوشِ — nūn sākin + fāʾ: ikhfāʾ.
الْعِهْنِ — the nūn is vowelled; no nūn-sākin rule applies there.