Question

Factorize: -
a^3(b+c) ^2+b^3(c+a) ^2+c^3(a+b) ^2

Answer 1

${a}^{3} (b + c) {}^{2} + {b}^{3} (c + a) {}^{2} + {c}^{3} {(a + b)}^{2}$


Using the identity (x+y)^2 = x^2+y^2+2xy


$\bf {a}^{3} + {b}^{2} + c {}^{2} + 2bc+ b {}^{3} + c {}^{2} + a {}^{2} \\ \: \bf + 2ac + {c}^3 + {a}^{2} + {b}^{2} + 2ab$


$\boxed{ \bf{taking \: like \: terms \: }}$



$\bf{a}^{3} + {b}^{3} + c {}^{3} + 2 {a}^{2} + 2 {b}^{2} + 2 {c}^{2} \\ \bf + 2ab + 2bc \: + 2ac$



$\boxed{ \bf{taking \: 2 \: common}}$


$\bf = > {a}^{3} + {b}^{3} + {c}^{3} + 2( {a}^{2} + {b}^{2} + {c}^{2} \\ \bf + ab + bc + ac)$




$\red{ \bf{hope \: it \: helps : )}}$