Question

The HCF of \(x^4 - y^4\) and \(x^6 - y^6\) is :

(a) \(x^2 - y^2\)

(b) \(x^2 + y^2\)

(c) \(x^3 + y^3\)

(d) \(x^3 - y^3\)

Answer 1

(a) x² - y²

x⁴ - y⁴ = (x² - y²)(x² + y²)

= (x - y)(x + y)(x²+ y²)

x⁶ - y⁶ = (x³)² - (y³)² = (x³ - y³)(x³ + y³)

∴ Reqd. HCF = (x - y )(x + y) = x² - y²