Question

Factorise : `1/4 ( a + b )^2 - 9/16 ( 2a - b )^2` 

Answer 1

`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 )`