Answer:
- (x² + 2y² + 2xy)(x² + 2y² - 2xy)
Step-by-step explanation:
Given binomial:
x⁴ + 4y⁴
In order to factorize it, follow the steps:
Complete the square:
- x⁴ + 4y⁴ =
- (x²)² + 2*(x²)*(2y²) + (2y²)² - 2*(x²)*(2y²) =
- (x² + 2y²)² - (2xy)² =
- (x² + 2y² + 2xy)(x² + 2y² - 2xy)
Used identities:
- (a + b)² = a² + 2ab + b²
- a² - b² = (a + b)(a - b)
