Question

factorize x⁴+y4-27x²y²​

Answer 1

Answer:

(x2+5xy−y2)(x2−5xy−y2)

  x4+y4−27x2y2

=(x2)2−2x2y2+(y2)2−25x2y2

=(x2−y2)2−(5xy)2

=(x2+5xy−y2)(x2−5xy−y2)

Answer 2

Answer:

Step-by-step explanation:

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)