Question

factories a sq +b sq + 2ab +2bc +2ca​

Answer 1

$\Large\underline{\underline{\sf{\green{Question:}}}}$

a² + b² + 2ab + 2bc + 2ca

$\Large\underline{\underline{\sf{\green{Required \; solution:}} } }$

Formula Used : a² + b² + 2ab = (a + b)²

$\sf In~ order~ to~ factorise~ following~ term, \\ \sf we~ have~ to ~break ~equation~ in~ two~ parts.$

First Part : a² + b² + 2ab and Second Part : + 2bc + 2ca

First Part : (a + b)² and Second Part : 2c(a + b)

$\sf Keeping~ both~parts~ together~ we~ get,$

$\implies \sf{ (a + b)^2 + 2c(a + b)}$

$\sf Taking ~(a + b) ~as~ common~ we~ get,$

$\implies \sf (a + b)[ (a + b) + 2c ]$

$\implies \sf (a + b)(a + b + 2c)$

$\sf{Hence,}$

$\sf factorised ~form ~of~ a^2 + b^2 + 2ab + 2bc + 2ca~ \\\sf into~ (a + b)(a + b + 2c).$

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Hope it helps :)