Question
Factorise : $9(a - 2)^2- 16(a + 2)^2$
✓
Answer
$9(a - 2)^2- 16(a + 2)^2$
$= [ 3( a - 2 )]^2 - [4( a + 2 )]^2$
$= [ 3( a - 2 ) - 4( a + 2 )][ 3( a - 2) + 4( a + 2 )]$
$[ \because a^2 - b^2 = ( a + b )( a - b )]$
$= [ 3a - 6 - 4a - 8 ][ 3a - 6 + 4a + 8 ]$
$= ( - a - 14 )( 7a + 2 )$
$= - ( a + 14 )( 7a + 2 )$
$= [ 3( a - 2 )]^2 - [4( a + 2 )]^2$
$= [ 3( a - 2 ) - 4( a + 2 )][ 3( a - 2) + 4( a + 2 )]$
$[ \because a^2 - b^2 = ( a + b )( a - b )]$
$= [ 3a - 6 - 4a - 8 ][ 3a - 6 + 4a + 8 ]$
$= ( - a - 14 )( 7a + 2 )$
$= - ( a + 14 )( 7a + 2 )$
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