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