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Question
Factorise : 25(2a - b)2 - 81b2
Solution
25(2a - b)2 - 81b2
= [ 5( 2a - b )]2 - (9b)2
= [ 5( 2a - b ) - 9b ][ 5( 2a - b ) + 9b ]
[ ∵ a2 - b2 = ( a + b )( a - b )]
= [ 10a - 5b - 9b ][ 10a - 5b + 9b ]
= [ 10a - 14b ][ 10a + 4b ]
= 2 x ( 5a - 7b ) x 2 x ( 5a + 2b )
= 4( 5a - 7b )( 5a + 2b )
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