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factorize that x^4+4y^4​

Sagot :

Mhanifaidn

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)
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