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