Question

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Answer 1

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$3 {a}^{2} - {b}^{2} - {c}^{2} + 2ab - 2bc + 2ca \\ \\ \implies \: 4 {a}^{2} - {a}^{2} - {b}^{2} - {c}^{2} + 2ab - 2bc + 2ac \\ \\ \implies4 {a}^{2} - ( {a}^{2} + {b}^{2} + {c}^{2} - 2ab + 2bc - 2ac) \\ \\ \implies \: (2a {)}^{2} - (a - b - c {)}^{2} \\ \\ \implies(2a + a - b - c)(2a - a + b + c) \\ \\ \implies(3a - b - c)(a + b + c)$

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Answer 2

3a2-b2-c2+2ab-2bc+2ca

3a²−b²−c²+2ab−2bc+2ac 
=4a²−a²−b²−c²+2ab−2bc+2ac 
=4a²−(a²+b²+c²−2ab+2bc−2ac) 
=(2a)²−(a−b−c)² 
=(2a+a−b−c)(2a−a+b+c) 
=(3a−b−c)(a+b+c)