Question

(5a + 2b)^2-(3a-2b)^2​

Answer 1

16a^2+32ab is the right answer...

Answer 2

To simplify -

=> ( 5a + 2b )² - ( 3a - 2b )² .

Solution -

=> ( 5a + 2b )² - ( 3a - 2b )²

=> [ 25a² + 20ab + 4b² ] - [ 9a² - 12ab + 4b² ]

=> 25a² + 20ab + 4b² - 9 a² + 12ab - 4b²

=> [ 25a² - 9a² ] + [ 20ab + 12ab ] + [ 4b² - 4b² ]

=> 16a² + 32 ab

Hence , Option A is the correct answer .

_________________________________

Additional Information -

( a + b )² = a² + 2ab + b²

( a - b )² = a² - 2ab + b²

( a + b )( a - b ) = a² - b²

( a + b )³ = a³ + 3ab ( a + b ) + b³

( a - b )³ = a³ - 3ab ( a + b ) - b³

( a + b + c )³ = a³ + b³ + c³ + 3 ( a + b )( b + c )( c + a )

a³ + b³ + c³ - 3abc = ( a + b + c )( a² + b² + c² - ab - bc - ca )

When a + b + c = 0 ,

a³ + b³ + c³ = 3abc .

_________________________________