Question
Factorise:
$4 a^2-4 b^2+4 a+1$
$4 a^2-4 b^2+4 a+1$
✓
Answer
$4 a^2-4 b^2+4 a+1$
$=\left(4 a^2+4 a+1\right)-4 b^2$
$=\left[(2 a)^2+2 \times 2 a \times 1+(1)^2\right]-(2 b)^2$
$=(2 a+1)^2-(2 b)^2$
$=(2 a+1-2 b)(2 a+1+2 b)$
$=(2 a-2 b+1)(2 a+2 b+1)$
$=\left(4 a^2+4 a+1\right)-4 b^2$
$=\left[(2 a)^2+2 \times 2 a \times 1+(1)^2\right]-(2 b)^2$
$=(2 a+1)^2-(2 b)^2$
$=(2 a+1-2 b)(2 a+1+2 b)$
$=(2 a-2 b+1)(2 a+2 b+1)$
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