Question

Factorise: 4 a square minus 4 b square + 4a + 1

Answer 1

4a²-4b²+4a+1
=[(2a)²+1+2×1×2a] -(2b)²
=[2a+1]²-[2b]²
=(2a+1-2b)(2a+1+2b)

Answer 2

The factorisation of $4a^2-4b^2+4a+1$ is $(2a+1+2b)(2a+1-2b).$.

Step-by-step explanation:

We have,

$4a^2-4b^2+4a+1$

To find, the factorisation of $4a^2-4b^2+4a+1=?$

∴ $4a^2-4b^2+4a+1$

$=(4a^2+4a+1)-4b^2$

$=((2a)^2+4(2a)(1)+1^{2} )-(2b)^2$

$=(2a+1)^2-(2b)^2$

[ ∵ $(a+b)^{2}=a^{2} +2ab+b^{2}$]

$=(2a+1+2b)(2a+1-2b)$

[ ∵ $a^{2} -b^{2} =(a+b)(a-b)$]

Hence, the factorisation of $4a^2-4b^2+4a+1$ is $(2a+1+2b)(2a+1-2b).$.