Question

Factorise 25(x+y)²-9(x-y) ²

Answer 1

25 x² + 25 y² + 50 xy - 9 x² - 9 y² + 18 x y
= 16 x² + 16 y² + 68 x y 
= 4 (4 x² + 17 x y + 4 y²)
= 4 ( 4x + y) (x + 4 y)

Another way:  
  we use a² - b² = (a+b) (a-b)
  
so  25 (x+y)²  - 9 (x-y)²
 =  [ 5(x+y)  + 3 (x-y) ] * [ 5 (x+y)  - 3 (x-y) ]
 =  [ 8 x + 2 y ] * [ 2 x + 8 y]
 = 4 * (4x + y) (x + 4y)
         

Answer 2

25(x +y)^2 -9(x -y)^2

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

=>{5(x + y) -3(x - y)}{5(x + y) + 3(x - y)}

=> (5x +5y -3x+3y )(5x +5y+3x-3y)

=>(2x +8y ) (8x +2y)

=>4(x + 4y)(4x + y)