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Grade 10Algebra

a factor of [a+b+c]3 - a3-b3-c3? with solution..

abhijith padala

13 Years agoGrade 10

1 Answer

Arun Kumar

12 Years ago

Hi
$\\(a+b+c)3 - a^3 - b^3 - c^3 \\= a^3 + b^3 + c^3 + 3ab(a+b) + 3bc(b+c) + 3ac(a+c) + 6abc -a^3 -b^3 -c^3 \\= 3ab(a+b) + 3bc(b+c) + 3ac(a+c) + 6abc \\= 3( ab(a+b) + bc(b+c) + ac(a+c) + 2abc) \\= 3( ab(a+b) + b^2c + abc + bc^2 + ac^2 + a^2c + abc) \\=3( ab(a+b) +bc(a+b) +c2(a+b) + ac(a+b)) \\=3(a+b)(c^2 + bc + ab + ac) \\=3(a+b)( c(b+c) + a(b+c)) \\=3(a+b)(b+c)(c+a)$
Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

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