Respuesta :

Answer:

[tex]4a^{2} + b^{2}  - c^{2}  + 4ab[/tex] [tex]= (2a + b -c) (2a + b+c)[/tex]

Step-by-step explanation:

Here, the given expression is [tex]4a^{2} + b^{2}  - c^{2}  + 4ab[/tex]

or, the given expression can be written as

 [tex](4a^{2} + b^{2}  + 4ab ) - c^{2}[/tex]

Now, by ALGEBRAIC IDENTITY: [tex](x+y)^{2}  = x^{2} + y^{2}  + 2xy[/tex]

So, similarly here, [tex](2a +b){2}  = 4a^{2} + b^{2}  + 4ab[/tex]

Hence, on simplification, the expression

[tex](4a^{2} + b^{2}  + 4ab ) - c^{2} = (2a + b)^{2} - c^{2}[/tex]

Now, by ALGEBRAIC IDENTITY: [tex](x +y)(x-y) = x^{2}  - y^{2}[/tex]

So, similarly  [tex](2a + b)^{2} - c^{2}[/tex][tex]= (2a + b -c) (2a + b+c)[/tex]

Hence, the given expression is factorized as:

[tex]4a^{2} + b^{2}  - c^{2}  + 4ab[/tex] [tex]= (2a + b -c) (2a + b+c)[/tex]

ayu350

The answer above has the correct explanation but a calculation mistake. Up to the part where it simplifies to [tex](2a-b)^{2} - c^{2}[/tex], everything is right.

Using the formula (a+b) (a-b), we get (2a-b-c)(2a-b+c). Not (2a+b-c) (2a+b+c)

So, the correct answer should be: (2a - b + c) (2a - b - c)

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