Question

Resolve into factors:1+a+b+c+ab+bc+ca+abc

Answer 1

Answers 1 + a + b + c + ab + bc + ca + abc =? Take a as common = 1+a(1+b+c+bc)+b+c+bc ........ (i) let x= b+c+bc therefore (i) will become, =1+a(1+x)+x = 1+x +a(1+x) take (1+x) as common = (1+x) (1+a) .............. (ii) 1+x = 1+b+c+bc ( WKT x=b+c+bc ) take b as common 1+x= 1+b(1+c)+c = 1+c+b(1+c) take (1+c) as common = (1+c)(1+b) therefore , 1+x = (1+c)(1+b) ....... (iii) sub (iii) in (ii) 1 + a + b + c + ab + bc + ca + abc = (1+a)(1+c)(1+b)

Answer 2

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