2 years ago

Factorize that x^4+4y^4

Mathematics

1 answer:

ipn [44]2 years ago

4 0

Answer:

(x² + 2y² + 2xy)(x² + 2y² - 2xy)

Step-by-step explanation:

<h3>Given binomial:</h3>

x⁴ + 4y⁴

In order to factorize it, follow the steps:

<h3>Complete the square:</h3>

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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Factorize that x^4+4y^4​

Factorize that x^4+4y^4