Q. 285.0( 1 Vote )

Factorize
(i) 9x2 – y2
(ii) (3 – x)2 – 36x2
(iii) (2x – 3y)2 – (3y + 4y)2
(iv) 16x4 – y4

Answer :

(i) 9x2 – y2 = (3x)2 – (y)2
               = (3x + y)(3x – y)


(ii) (3 – x)2 – 36x2 = (3 – x)2 – (6x)2
                             
= (3 - x + 6x) (3 - x - 6x)
                         = (3 + 5x)(3 – 7x)


(iii) (2x – 3y)2 – (3x + 4y)2 = (2x – 3y + 3x + 4y)(2x – 3y – 3x – 4y)
                                     = (5x + y)(- x – 7y) 
                                     = -(5x + y) (x + 7y)


(iv) 16x4 – y4 = (4x2)2 – (y2)
                      
= (4x2 + y2)(4x2 –y2)
                   = (4x2 + y2)(2x + y) (2x - y)

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