Question

$2ab - a {2} - b {2} + c {2}$

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Answer 1

Question :-

Factorize - $\sf 2ab - a^ {2} - b^ {2} + c^ {2}$

Identities used -

• $\sf a^2 + b^2 - 2ab = (a-b)^2$
• $\sf a^2 - b^2 = (a+b)(a-b)$

Solution :-

➩ $\sf 2ab - a^ {2} - b^ {2} + c^ {2}$

➩ $\sf = - [ a^2 + b^2 - 2ab - c^2]$

➩ $\sf = - [ (a - b)^2 - c^2]$

➩ $\sf = - [( a - b + c )(a - b - c)]$

➩ $\sf = (a-b+c)(b+c-a)$

Answer 2

Answer:

Question :-

$Factorize - \sf 2ab - a^ {2} - b^ {2} + c^ {2}$

Identities used -

$\sf a^2 + b^2 - 2ab = (a-b)^2a$

$➩ \sf = - [ a^2 + b^2 - 2ab - c^2]=−[a$

$➩ \sf = - [ (a - b)^2 - c^2]=−[(a−b)$

$➩ \sf = - [( a - b + c )(a - b - c)]=−[(a−b+c)(a−b−c)]$

$➩ \sf = (a-b+c)(b+c-a)=(a−b+c)(b+c−a)$