Question

a²+2a+b²-c² resolve into factors​

Answer 1

Answer:

Faxtorisationof

a

2

−2ab+b

2

−c

2

=(a−b+c)(a−b−c)

Step-by-step explanation:

\begin{gathered}Given \: expression \\a^{2}-2ab+b^{2}-c^{2}\\=(a^{2}-2ab+b^{2})-c^{2}\\ = (a-b)^{2}-c^{2}\end{gathered}

Givenexpression

a

2

−2ab+b

2

−c

2

=(a

2

−2ab+b

2

)−c

2

=(a−b)

2

−c

2

/* By algebraic identity:

\boxed { x^{2}-2xy+y^{2}=(x-y)^{2}}

x

2

−2xy+y

2

=(x−y)

2

*/

=[(a-b)+c][(a-b)-c][(a−b)+c][(a−b)−c]

/* By algebraic identity:

\boxed {x^{2}-y^{2}=(x+y)(x-y)}

x

2

−y

2

=(x+y)(x−y)

*/

=(a-b+c)(a-b-c)(a−b+c)(a−b−c)

Therefore,

\begin{gathered}Faxtorisation\: of\\ a^{2}-2ab+b^{2}-c^{2}\\=(a-b+c)(a-b-c)\end{gathered}

Faxtorisationof

a

2

−2ab+b

2

−c

2

=(a−b+c)(a−b−c)

Answer 2

Step-by-step explanation:

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