Question

factorise a^2+b^2-2(ab-bc-ca)​

Answer 1

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• factorise a^2+b^2-2(ab-bc-ca)

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$\large\fbox a^2 +b^ 2 +2(ab+bc+ca)=(a+b)(a+b+ 2c)$

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$=a^ 2 +b^ 2 +2ab+2bc+2ca$

Using identity a2+b2+2ab=(a+b)^ 2

$a^{2} +b^{2}+2ab=(a+b)^ 2$

We get,

$=(a+b)^ 2 +2bc+2ca$

$=(a+b)^ 2 +2c(b+a) \\ or \: (a + b) ^ 2 + 2c (a + b)$

$\large\fcolorbox{aqua}{aqua}{\underline{Taking (a + b) common }}$

$=(a+b)(a+b+2c)$

$a^ 2 +b^ 2 +2(ab+bc+ca)=(a+b)(a+b+ 2c)$

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