Question

factorise: x^4+x^2y^2+y^4​

Answer 1

Answer:

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)

⚡⚜Hope it will help you.⚜⚡