Question

Factorize:
a²+b²+2(ab+bc+ca)

Answer 1

Answer:

a^2+b^2+2(ab+bc+ca) = (a+b+2c)×(a+b)

Step-by-step explanation:

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

a^2+b^2+c^2+2ab+2bc+2ca-c^2

= (a+b+c)^2-c^2

= (a+b+c+c)×(a+b+c-c)

·.· a^2-b^2 = (a+b)×(a-b)

= (a+b+2c)×(a+b)

Answer 2

Given : a² + b² + 2(ab + bc + ca)

Now ,

a² + b² + 2ab + 2bc + 2ca

(a² + b² + 2ab) + (2bc + 2ca)

we know that , a² + b² + 2ab = (a + b)²  

= ( a + b)² + 2bc + 2ca

= ( a + b)² + 2c( b + a )

= ( a + b)² + 2c( a + b )

Here ( a + b ) is a common factor :  

= ( a + b )[ a + b + 2c ]

a² + b² + 2(ab + bc + ca)

Hence, the factorisation of a² + b² + 2(ab + bc + ca) is  ( a + b )[ a + b + 2c ].  

HOPE THIS ANSWER WILL HELP YOU…..

 

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