Question
Factorise: $a^4 - (a^2 - 3b^2)^2$
✓
Answer
$a^4 - (a^2 - 3b^2)^2$
$= (a^2)^2 - (a^2 - 3b^2)^2$
$= (a^2 + a^2 - 3b^2) (a^2 - a^2 + 3b^2)$
$= (2a^2 - 3b^2) (3b)^2$
$= 3b^2 (2a^2 - 3b^2)$
$= (a^2)^2 - (a^2 - 3b^2)^2$
$= (a^2 + a^2 - 3b^2) (a^2 - a^2 + 3b^2)$
$= (2a^2 - 3b^2) (3b)^2$
$= 3b^2 (2a^2 - 3b^2)$
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