Question

Factorize:
$a^2+b^2+2(ab+bc+ca)$

Answer 1

Given: $a^2+b^2+2(ab+bc+ca)$
$\therefore a^2+b^2+2(ab+bc+ca)$
$=a^2+b^2+2ab+2bc+2ca$
$=(a+b{)}^2+2c(b+a)$
$[\because a^2+b^2+2ab=(a+b{)}^2]$
$=(a+b)(a+b+2c)$
Hence, $a^2+b^2+2(ab+bc+ca)=(a+b)(a+b+2c).$