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Question
Factorise : `1/4 ( a + b )^2 - 9/16 ( 2a - b )^2`
Solution
`1/4 ( a + b )^2 - 9/16 ( 2a - b )^2`
=`1/4 [ ( a + b )^2 - 9/4( 2a - b )^2 ]`
=`1/4 [ ( a + b )^2 - [3/2( 2a - b )^2] ]`
=`1/4 [( a + b + 3/2(2a - b))( a + b - 3/2( 2a - b ))]`
=`1/4[( a + b + 3a - (3b)/2)( a + b - 3a + (3b)/2 )]`
= `1/4[( 4a - b/2 )( (5b)/2 - 2a )]`
= `1/4[(( 8a - b )/2)([ 5b - 4a ]/2)]`
= `1/4[ 1/4( 8a - b )( 5b - 4a )]`
= `1/16 ( 8a - b )( 5b - 4a )`
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