Question
Factorize : $9a^2- (a^2- 4)^2$
✓
Answer
$9a^2- (a^2 - 4)^2$
$= (3a)^2 - (a^2 - 4)^2$
$= [ 3a + (a^2 - 4)][ 3a - (a^2 - 4)]$
$= [ 3a + a^2 - 4 ][ 3a - a^2 + 4 ]$
$= [ a^2 + 3a - 4 ][- a^2 + 3a + 4]$
$= (a + 4)(a - 1)(-a^2+ 3a + 4)$
$=(a + 4)(a - 1)[-(a^2- 3a - 4)]$
$= - (a + 4)(a - 1)(a - 4)(a + 1)$
$= (a + 4)(a - 1)(a + 1)(4 - a).$
$= (3a)^2 - (a^2 - 4)^2$
$= [ 3a + (a^2 - 4)][ 3a - (a^2 - 4)]$
$= [ 3a + a^2 - 4 ][ 3a - a^2 + 4 ]$
$= [ a^2 + 3a - 4 ][- a^2 + 3a + 4]$
$= (a + 4)(a - 1)(-a^2+ 3a + 4)$
$=(a + 4)(a - 1)[-(a^2- 3a - 4)]$
$= - (a + 4)(a - 1)(a - 4)(a + 1)$
$= (a + 4)(a - 1)(a + 1)(4 - a).$
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