Question

How to factorise :-

4x^4+81y^4​

Answer 1

Answer:

( 2x² + 9y² + 6xy ) ( 2x² + 9y² - 6xy )

Step-by-step explanation:

To find -----> Factors of 4x⁴ + 81 y⁴

Solution------> We know that ,

4 x⁴ = ( 2 )² ( x² )²

= ( 2x² )²

81 y⁴ = ( 9 )² ( y² )²

= ( 9y² )²

Now ,

4x⁴ + 81y⁴ = ( 2x² )² + ( 9y² )²

Now , let , a = 2x² and b = 9y² , putting in above

= ( a )² + ( b )²

Now adding and subtracting 2ab , to make it perfect square ,

= ( a )² + ( b )² + 2 ab - 2ab

= ( a² + b² + 2ab ) - 2ab

We know that , ( x + y )² = x² + y² + 2xy , applying it , we get,

= ( a + b )² - 2 ab

= ( 2x² + 9y² )² - 2 ( 2x² ) ( 9y² )

= ( 2x² + 9y² )² - 36 x² y²

= ( 2x² + 9y² )² - ( 6xy )²

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

= ( 2x² + 9y² + 6xy ) ( 2x² + 9y² - 6xy )

Answer 2

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