Question

Factorise each of the following;16(x+y)^2-25(x-3y)^2

Answer 1

Step-by-step explanation:

Given---> 16 ( x + y )² - 25 ( x - 3y )²

To find ---> Factorize given expression

Solution---> We have an identity,

a² - b² = ( a + b ) ( a - b )

We know that ,

16 = 4 × 4

25 = 5 × 5

Now,

16 ( x + y )² - 25 ( x - 3y )²

= ( 4 )² ( x + y )² - ( 5 )² ( x - 3y )²

= { 4 ( x + y ) }² - { 5 ( x - 3y ) }²

= ( 4x + 4y )² - ( 5x - 15y )²

Applying above identity, we get

={ ( 4x + 4y ) + ( 5x - 15y ) } { ( 4x + 4y ) - ( 5x - 15y ) }

= ( 4x + 4y + 5x - 15y ) ( 4x + 4y - 5x + 15y )

= ( 9x - 11 y ) ( 19y - x )

Additional information--->

1) (a + b )² = a² + b² + 2ab

2) ( a - b )² = a² + b² - 2ab