Question

factorise 25 (X+y)2-16(x-y)2​

Answer 1

Answer:

( 9x + y ) ( x + 9y )

Step-by-step explanation:

Given---> 25 ( x + y )² - 16 ( x - y )²

To find---> Factors of given expression

Solution----> We know that,

a² - b² = ( a + b ) ( a - b ) and

25 = 5 × 5 = 5²

16= 4 × 4 = 4²

Now,

25 ( x + y )² - 16 ( x - y )²

= ( 5 )² ( x + y )² - ( 4 )² ( x - y )²

= { 5 ( x + y ) }² - { 4 ( x - y ) }²

= ( 5x + 5y )² - ( 4x - 4y )²

Applying above identity we get,

={ ( 5x + 5y ) + ( 4x - 4y ) } { ( 5x + 5y ) - ( 4x - 4y ) }

=( 5x + 5y + 4x - 4y ) ( 5x + 5y - 4x + 4y )

= ( 9x + y ) ( x + 9y )

Additional identities--->

1) ( x + a ) ( x + b ) = x² + ( a + b ) x + ab

2) a³ + b³ = ( a + b ) ( a² + b² - ab )

3) a³ - b³ = ( a - b ) ( a² + b² + ab )

4) ( a + b )³ = a³ + b³ + 3ab ( a + b )

5) ( a - b )³ = a³ - b³ - 3ab ( a - b )

6) ( a + b )² = a² + b² + 2ab

7) ( a - b )² = a² + b² - 2ab

#Answerwithquality

#BAL

Answer 2

Answer:

answer will be (9x+y) (x+9y)

hope it will help you