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:

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