n : To factorise : > [ ¼ ( x + y )² ] - [ 9/16 ( x - y )² ] Each of the terms can be expressed as as square ; > [ ½ ( x + y ) ]² - [ ¾ ( x - y ) ]² . The expression , a² - b² can be written as ( a + B )( a - b ) > [ ½ ( x + y ) ]² - [ ¾ ( x - y ) ]² . > [ ½ ( x + y ) + ¾( x - y) ][ ½( x + y ) - ¾( x - y) ] > [ ½ x + ½ y + ¾ x - ¾ y ] [ ½ x + ½ y - ¾ x + ¾ y ] > [ 5/4 x + ¼ y ][ ¼ x + 5/4 y ] This is the REQUIRED answer . ________________________________________ Additional Information : (a + b)² = a² + 2ab + b² (a + b)² = (a - b)² + 4AB (a - b)² = a² - 2ab + b² (a - b)² = (a + b)² - 4ab a² + b² = (a + b)² - 2ab a² + b² = (a - b)² + 2ab 2 (a² + b²) = (a + b)² + (a - b)²4ab = (a + b)² - (a - b)² ab = {(a + b)/2}² - {(a-b)/2}²(a + b + c)² = a² + b² + c² + 2(ab + bc + CA) (a + b)³ = a³ + 3a²b + 3ab² b³(a + b)³ = a³ + b³ + 3ab(a + b) (a - b)³ = a³ - 3a²b + 3ab² - b³a³ + b³ = (a + b)( a² - ab + b² )a³ + b³ = (a + b)³ - 3ab( a + b)a³ - b³ = (a - b)( a² + ab + b²)a³ - b³ = (a - b)³ + 3ab ( a - b )________________________________________