Question

Factorize (b + c)(c + a)(a +b) + abc​

Answer 1

Step-by-step explanation:

(a+b)(b+c)(c+a)+abc

= (ab+b²+ac+bc)(c+a)+abc

=c(ab+b²+ac+bc)+a(ab+b²+ac+bc)+abc

=abc+b²c+ac²+bc²+a²b+ ab²+a²c+abc+abc

=abc+abc+abc+a²b+ab²+b²c+bc²+a²c+ac²

=3abc+ a²b+ab²+a²c+b²c+bc²+ac²

=3abc+ab(a+b)+c(a²+b²)+c²(b+a)

=3abc+ab(a+b)+c {(a+b)²-2ab}+c²(a+b)

=3abc+ab(a+b)+(a+b)²c-2abc+c²(a+b)

=3abc-2abc+ab(a+b)+ c(a+b)²+c²(a+b)

....×××××××

=abc-[(a+b) {ab+c(a+b)+c²}].

=abc-[(a+b){ab+ac+bc+c²}]

=abc-[(a+b){ab+bc+ac+c²}]

=abc-[(a+b){b(a+c)+c(a+c)}]

=abc-[(a+b)(a+c)(b+c)]

Wherever possible I have tried to break and factorise it .Hope it will help you something.❤️❤️❤️❤️❤️❤️❤️❤️❤️