Question

Factorize : a^2 + b^2 + 2ab + 2bc + 2ca

Answer 1

Answer:

(a + b)(a + b + 2c)

Step-by-step explanation:

The given expression can be factorised as follows:

a² + b² + 2ab + 2bc + 2ac

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

Applying formula,we get  

⇒(a + b)² + 2(bc + ca)  

Looking for common sub-expressions : (a + b)

⇒(a + b)² + 2c(b + a)  

⇒(a + b) (a + b + 2c)  

Can't be factorized any more.

Hence, Final result of a² + b² + 2ab + 2bc + 2ca is (a + b)(a + b + 2c).

Answer 2

The correct answer is (a + b)(a + b + 2c).

Given: The equation = $a^{2} +b^{2} +2ab+2bc+2ca$.

To Find: The factors of the equation.

Solution:

$a^{2} +b^{2} +2ab+2bc+2ca$

As we know the identity: $(a+b)^{2} =a^{2} +b^{2} +2ab$.

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

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

Taking (a + b) common.

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

Hence, the factors are (a + b)(a + b + 2c).

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