Question

plz solve it!!!
show that submission of ab [a + b]+ 2ab=[a+b][b+c][c+a]. Give the answer in detail

Answer 1

Excuse me,

but something is left out in the question.

Answer 2

Summation of ab [a + b]+ 2abc=[a+b][b+c][c+a]

Proof is given below:

To Show That

$\Sigma ab(a+b)+2abc=(a+b)(b+c)(c+a)$

LHS

$=\Sigma [ab(a+b)]+2abc$

$=ab(a+b)+bc(b+c)+ca(c+a)+2ab$

$=a^2b+ab^2+b^2c+bc^2+c^2a+ca^2+abc+abc$

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

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

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

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

= RHS                                                     (Proved)

Hope this answer is helpful.

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