Question

y^6 - x^ 6 ÷ x² - y²

what is answer this question?

Answer 1

(y^6 -x^6 )÷(x^2 -y^2)
=-(x^6 -y^6 )÷(x^2 -y^2)
= -{(x^2)^3 -(y^2)^3} ÷(x^2 -y^2)
By using the identity a^3 -b^3 = (a-b)(a^2 + ab+b^2)
=-(x^2- y^2) {(x^2)^2 +x^2y^2 +(y^2)^2}÷(x^2 -y^2)
= -(x^2 -y^2)(x^4 +x^2y^2+y^4) ÷ (x^2 -u^2)
= - (x^4 +x^2y^2+y^4) 

Answer 2

(y^6 - x^6)/(x² - y²)

= -{(x²)³ - (y²)³}/(x² - y²)

[ use, a³ - b³ = (a -b)(a² + b² + ab) ]

= -(x² - y²){(x²)² + (y²)² +x²y²}/(x² - y²)

= -(x⁴ + y⁴ +x²y²)