Question

3–12(x−y)^2 factorise​

Answer 1

Answer:

3 ( 1 + 2x - 2y ) ( 1 - 2x + 2y )

Step-by-step explanation:

Given----> 3 - 12 ( x - y )²

To find -----> Factorise the given expression

Solution-----> ATQ ,

3 - 12 ( x - y )²

=> 3 { 1 - 4 ( x - y )² }

=> 3 { ( 1 )² - ( 2 )² ( x - y )² }

=> 3 [ ( 1 )² - { 2 ( x - y ) }² ]

=> 3 { ( 1 )² - ( 2x - 2y )² }

We know that,

a² - b² = ( a + b ) ( a - b ) , applying it we get ,

=> 3 { 1 + ( 2x - 2y ) } { 1 - ( 2x - 2y ) }

=> 3 ( 1 + 2x - 2y ) ( 1 - 2x + 2y )

Additional information---->

1) ( a + b )² = a² + b² + 2ab

2) ( a - b )² = a² + b² - 2ab

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

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

5) ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca