Factorize 1+a+b+c+ab+bc+ca+abc
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1+a+b+c+ab+bc+ca+abc
= abc+ab+bc+ca+a+b+c+1
=ab(c+1)+c(b+a)+(a+b)+(c+1)
=ab(c+1)+(c+1)}+{c(b+a)+(a+b)}
= (c+1)(ab+1)+(b+a)(c+1)
=(c+1){ab+1+b+a}
= abc+ab+bc+ca+a+b+c+1
=ab(c+1)+c(b+a)+(a+b)+(c+1)
=ab(c+1)+(c+1)}+{c(b+a)+(a+b)}
= (c+1)(ab+1)+(b+a)(c+1)
=(c+1){ab+1+b+a}
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