Question

Chứng min đẳng thức

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

Answer 1

$(a+b+c{)^}^3=((a+b)+c{)^}^3=(a+b{)^}^3+{\mathrm{c^}}^3+3(a+b\left)c\right(a+b+c)$
$={\mathrm{a^}}^3+{\mathrm{b^}}^3+3ab(a+b)+{\mathrm{c^}}^3+3(a+b)c(a+b+c)$
$={\mathrm{a^}}^3+{\mathrm{b^}}^3+{\mathrm{c^}}^3+3(a+b)(ab+c(a+b+c\left)\right)$
$={\mathrm{a^}}^3+{\mathrm{b^}}^3+{\mathrm{c^}}^3+3(a+b)(ab+ac+bc+{\mathrm{c^}}^2)$
$={\mathrm{a^}}^3+{\mathrm{b^}}^3+{\mathrm{c^}}^3+3(a+b)(a+c)(b+c)$