Question

factorise : x⁴+2x³y-2 xy³ - y⁴

pls answer the question.​

Answer 1

This can be factored by completing the square.

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

x² + x²y² +y4 first term and 3rd term are perfect squares

= (x²)² + x³y² + (y²)² the middle term

should to be 2x²y² to make

square, so add x²y² - x²y²

it a perfect

= (x²)² + x³y² + (y²)² + x²y² - x²y² combine 2nd and 4th terms = (x²)² + 2 x³y² + (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)