Question

Factorize that x^4+4y^4​

Answer 1

• (x² + 2y² + 2xy)(x² + 2y² - 2xy)

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)