Question

a2(b+c)+b2(c+a)+c2(a+b)+2abc

Answer 1

Hello buddy..
Check out this solution..

1. a^2(b+c)+b^2(c+a)+c^2(a+b)+2abc 
= a^2 b+ a^2c + b^2 c+ ab^2+c^2a+bc^2+2abc
= a(b^2+ 2bc+c^2) + a^2 b+ a^2c + b^2 c +bc^2
= a(b+c)^2 + a^2(b+c) + bc(b+c)
= (b+c) [ a^2 +a(b+c)+ bc]
= (b+c) (a +b)(c+a)

Hope it helps you buddy

Answer 2

(a + c)(b + c)(a + b) is the required answer of the given expression.

Step-by-step explanation:

                             $a^{2} (b+c)+b^{2} (c+a)+c^{2} (a+b)+2ab$

Solving above expression.

Now,

                        = $a^{2} b+ a^{2} c+ b^{2} c+ c^{2} a+ c^{2} a+ c^{2} b+2abc$

                         = $b(a^{2} + b^{2} + 2ab) + c(a^{2} +b^{2}) +a(b^{2}+c^{2} )$

                         = $b(a+c)+b^{2} (c+a)+ac^{2} +ca^{2}$

                         = $(a+c)((a+c)b +b^{2} +ac)$

                         = $(a+c)(ab+bc+b^{2}+ ac)$

                         = $(a+c)(c(a+b)+b(a+b))$

                         = (a+c)(b+c)(a+b)

Hence required equation.

Using just simple bodmass technique.