Question

factorise 1+ a+b+c+ab+bc+ca+abc

Answer 1

1+a+b+c+ab+bc+ca+abc
By rearranging
1+c+a+ca+b+bc+ab+abc
1(1+c)+a(1+c)+b(1+c)+ab(1+c)
(1+c)(1+a+b+ab)
(1+c){1(1+a)+b(1+a)}
(1+c){(1+a)(1+b)}
(1+a)(1+b)(1+c)  Answer

hope it helps!!☺☺

Answer 2

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)