Question

Factor completely: 4a^2+b^2−c^2+4ab

Answer 1

Answer:

$4a^{2} + b^{2}  - c^{2}  + 4ab$ $= (2a + b -c) (2a + b+c)$

Step-by-step explanation:

Here, the given expression is $4a^{2} + b^{2}  - c^{2}  + 4ab$

or, the given expression can be written as

 $(4a^{2} + b^{2}  + 4ab ) - c^{2}$

Now, by ALGEBRAIC IDENTITY: $(x+y)^{2}  = x^{2} + y^{2}  + 2xy$

So, similarly here, $(2a +b){2}  = 4a^{2} + b^{2}  + 4ab$

Hence, on simplification, the expression

$(4a^{2} + b^{2}  + 4ab ) - c^{2} = (2a + b)^{2} - c^{2}$

Now, by ALGEBRAIC IDENTITY: $(x +y)(x-y) = x^{2}  - y^{2}$

So, similarly  $(2a + b)^{2} - c^{2}$$= (2a + b -c) (2a + b+c)$

Hence, the given expression is factorized as:

$4a^{2} + b^{2}  - c^{2}  + 4ab$ $= (2a + b -c) (2a + b+c)$

Answer 2

The answer above has the correct explanation but a calculation mistake. Up to the part where it simplifies to $(2a-b)^{2} - c^{2}$, 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)