Question

prove that (a+b+c)^-a^-b^-c^=3(a+d)(b+c)(c+a)​

Answer 1

Answer:

Solution to (a +b +c)3 -a3 -b3 – c3 =3(a +b)(b +c)(c +a)

Step-by-step explanation:

(a+b+c) 3=[(a+b)+c]

3 =(a+b) 3+3(a+b)

2 c+3(a+b)c 2+c 3

=>(a+b+c) 3=(a 3+3a 2b+3ab 2 +b 3 )+3(a 2+2ab+b )c+3(a+b)c 2 +c 3

=>(a+b+c) 3

=a 3 +b 3 +c 3 +3a 2 b+3a 2 c+3ab 2 +3b 2 c+3ac

2 +3bc 2+6abc

=>(a+b+c) 3 =a 3+b 3 +c 3 +3a 2 b+3a 2

c+3ab 2 +3b 2c+3ac 2 +3bc 2 +3abc+3abc

=>(a+b+c) 3

=a 3 +b 3 +c 3

+3a(ab+ac+b 2

+bc)+3c(ab+ac+b 2 +bc)

=>(a+b+c) 3

=a 3+b 3 +c 3

+3(a+c)(ab+ac+b 2+bc)

=>(a+b+c) 3

=a 3

+b 3

+c 3

+3(a+c)[a(b+c)+b(b+c)]

=>(a+b+c) 3 =a 3 +b 3 +c 3

+3(a+c)(b+c)(a+b)

=>(a+b+c) 3−a 3 −b −c 3

=3(a+c)(b+c)(a+b)

Hence,proved.

Answer 2

L.H.S.

(a+b+c)³-a³-b³-c³ (a+b)³+c³+3(a+b)²c+3(a+b).c²-a³-b³-c³

a³+b³+3a²b+3ab²+c³+3(a+b)c(a+b+c)-a³-b³-c³

3ab(a+b)+3(a+b)c(a+b+c)

3(a+b)[ab+ac+bc+c²]

3(a +b)[a(b+c)+c(b+c)]

3(a+b)[(b+c)(a+c)]

3(a+b)(b+c)(c+a)

Hence proved .