Question

Factorize:625a^4 + 4b^4​

Answer 1

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a⁴ + 4b⁴ = (a²  + 2b² + 2ab)( (a²  + 2b² - 2ab) written as product of two factors

a⁴ + 4b⁴

= (a²)²  + (2b²)²

= (a²  + 2b²)²  - 2a²2b²

= (a²  + 2b²)²  - (2ab)²

= (a²  + 2b² + 2ab)( (a²  + 2b² - 2ab)

a⁴ + 4b⁴ = (a²  + 2b² + 2ab)( (a²  + 2b² - 2ab)

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Answer 2

(625 • (a4)) + 22b4

54a4 + 22b4

Final result :

625a4 + 4b4