Question

Factorise completely: 256x17 y2 – xy2.​

Answer 1

Answer:

xy²(16x⁸+1) (4x⁴+1) (2x²+1) (2x²-1 )

Step-by-step explanation:

Given----> 256 x¹⁷ y² - x y²

To find ---> Factors of given expression

Solution----> We know that,

a² - b² = ( a + b ) ( a - b ) and

16² = 256

4² = 16

2² = 4

Now,

256x¹⁷ y² - xy² = x y² ( 256 x¹⁶ - 1 )

= xy² { ( 16 x⁸ )² - ( 1 )² }

Applying above identity , we get,

= xy² ( 16x⁸ + 1 ) ( 16x⁸ - 1 )

= xy² ( 16x⁸ + 1 ) { ( 4x⁴ )² - ( 1 )² }

Applying above identity, we get,

= xy² ( 16x⁸ + 1 ) ( 4x⁴ + 1 ) ( 4x⁴ - 1 )

= xy² ( 16x⁸ + 1 ) ( 4x⁴ + 1 ) { (2x²)² - ( 1 )² }

Again applying above identity, we get,

=xy² (16x⁸+1 ) (4x⁴+1) (2x²+1 ) ( 2x² - 1 )

#Answerwithquality

#BAL

Answer 2

Answer:

Step-by-step explanation:

Given----> 256 x¹⁷ y² - x y²

To find ---> Factors of given expression

Solution----> We know that,

a² - b² = ( a + b ) ( a - b ) and

16² = 256

4² = 16

2² = 4

Now,

256x¹⁷ y² - xy² = x y² ( 256 x¹⁶ - 1 )

= xy² { ( 16 x⁸ )² - ( 1 )² }

Applying above identity , we get,

= xy² ( 16x⁸ + 1 ) ( 16x⁸ - 1 )

= xy² ( 16x⁸ + 1 ) { ( 4x⁴ )² - ( 1 )² }

Applying above identity, we get,

= xy² ( 16x⁸ + 1 ) ( 4x⁴ + 1 ) ( 4x⁴ - 1 )

= xy² ( 16x⁸ + 1 ) ( 4x⁴ + 1 ) { (2x²)² - ( 1 )² }

Again applying above identity, we get,

=xy² (16x⁸+1 ) (4x⁴+1) (2x²+1 ) ( 2x² - 1 )

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