How can A'BC'D + ABC'D = BD

(Boolean Algebra)

How can A'BC'D + ABC'D = BD

It can't.

A'BD + ABD = BD

A'BC'D + ABC'D + A'BCD + ABCD = BD

But A'BC'D + ABC'D = BC'D (not BD)

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EDIT: Additional Details

Note that in boolean algebra: A = A + A

ABCD + A'B'CD + ABC'D + A'BC'D + ABCD' + A'BC'D' + A'BCD + A'B'C'D'

First rearrange:
= (A'BC'D' + A'B'C'D') + (A'BCD + A'B'CD) + (ABCD + ABCD') + (ABC'D + A'BC'D)

Recall that adding the same value twice does not change equality (A = A + A)
= (A'BC'D' + A'B'C'D') + (A'BCD + A'B'CD) + (ABCD + ABCD') + (ABC'D + A'BC'D + A'BCD + ABCD)

= A'C'D' + A'CD + ABC + BD


-- Ματπmφm --

it doesn't. It = YXB+2(A).
Analyze the question more carefully.