How to solve $(a+bc)(d'+bc)(a'+d')$ using Boolean algebra

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I have done this. is this correct? If wrong, what is needed to be changed?

$(a+bc)(d'+dc)(a'+d')$

$ = ad'a' + abcd' + bcd'a' + bcbcd'$

$ = d' + abcd' + bcd'a' + bcbcd'$

$ = d' + bcd' (a + a' + bc)$

$ = d' + bcd' \cdot (1)$

$ = d'(1+bc)$

$ = d'$