factorise 1+a+c+ab+dc+ca+abc
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Factorization of 1 + a + b + c + ab + bc + ca + abc = (1+a) (1+b) (1+c)
Solution:
Writing the question and breaking it in simpler form to make common to adjust the numbers easily.
1 + c + a + ca + b + bc + ab + abc
Taking (1 + c) common we get the first factor the question now move onto the next factors:
= 1(1+c) + a(1+c) + b(1+c) + ab(1+c)
After shifting the factors the other factor contains,
= (1+c)(1+a+b+ab)
Shifting the factor (1+ a + b + ab) and taking (1 + a) common we get,
= 1 (1+a) + b (1+a)
= (1+c) {1 (1+a) + b (1+a) }
After taking (1 + a) we get the factors as: (1+c) (1+a) (1+b)
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