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Question

Simplify the following expression:
(ab+bc)(abbc)+(bc+ca)(bcac)+(ca+ab)(acab)

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Solution

Given expression,
(ab+bc)(abbc)+(bc+ca)(bcac)+(ca+ab)(acab)

Using the identity,
(a+b)(ab)=a2b2,

the given expression can be simplified as
(ab)2(bc)2+(bc)2(ac)2+(ac)2(ab)2

By grouping the like terms, this can be further simplified as follows:

[(ab)2(ab)2]+[(bc)2(bc)2]+[(ac)2(ac)2]=0

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