Question

factorise: x⁴+y⁴ - 27 x²y²​

Answer 1

This can  be factored by completing the square. 

Recall that perfect square trinomial  x²+2xy+y² = (x+y)².

x⁴ + x²y² +y⁴                      first term and 3rd term  are perfect squares

= (x²)² +  x²y² + (y²)²          the middle term should to be 2x²y²  to make                                                              it a perfect square, so add x²y² - x²y² 

= (x²)² +  x²y² + (y²)²  + x²y² - x²y²       combine 2nd and 4th terms

= (x²)² +  2 x²y² + (y²)²  - x²y²      first 3 terms form a perfect square trionomial

= (x² + y²)²- (xy)²                   it is a difference of two squares, now factor

=(x² + y² + xy)(x² + y² - xy)

Answer 2

IT IS A SQUARE OF X

$( ) {{x}^{2} - {x}^{2}}^{2}$

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