Factorise:

$25 (2 a - b)^{2} - 81 b^{2}$

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Solution

we know the algebraic identity

x² - y² = ( x + y )(x - y )

Now ,

25(2a - b )² - 81b²

= [ 5 ( 2a - b )]² - ( 9b)²

= ( 10a - 5b )² - ( 9b )²

= ( 10a - 5b + 9b )(10a -5b - 9b )

= ( 10a + 4b ) ( 10a - 14b )

= [ 2 ( 5a + 2b ) ] [ 2( 5a - 7b )]

= 4(5a + 2b )(5a - 7b )

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