Question

Factorise 25 (x+y)^2-x^2+4xy-4y^2

Answer 1

Answer:

3 ( 2x + y ) ( 4x + 7y )

Step-by-step explanation:

Given---> 25 ( x + y )² - x² + 4 xy - 4 y²

To find---> Factors of given expression

Solution---> We know that,

1) a² - 2ab + b² = ( a - b )²

2) a² - b² = ( a + b ) ( a - b )

ATQ,

25 ( x + y )² - x² + 4 xy - 4 y²

= ( 5 )² ( x + y )² - ( x² - 4 xy + 4y² )

= { 5 ( x + y ) }² - { ( x )² - 2 ( x ) ( 2y ) + ( 2y )² }

Applying first identity , we get,

= ( 5x + 5y )² - ( x - 2y )²

Applying second identity , we get,

= { ( 5x + 5y ) + ( x - 2y ) } { ( 5x + 5y ) - ( x - 2y ) }

= ( 5x + 5y + x - 2y ) ( 5x + 5y - x + 2y )

= ( 6x + 3y ) ( 4x + 7y )

Taking 3 , common from first bracket, we get,

= 3 ( 2x + y ) ( 4x + 7y )