Question

The factors of (x⁴ - 7x²y² + y⁴) are

(a) (x² + y² - 3xy)(x² + y² + 3xy)

(b) (x² - y² + 3xy)(x² + y² - 3xy)

(c) (x²- 3xy + y²)(x²  - 3xy - y²)

(d) (x² + 3xy + y²)(x²  - 3xy - y²)

Answer 1

(a) (x² + y² +3xy)(x² + y² - 3xy)

x⁴ - 7x²y² + y⁴

= x⁴ + 2x²y² + y⁴ - 9x²y²

= (x² + y²)² - (3xy)²

= (x² + y² +3xy)(x² + y² - 3xy)