Factorise x^12 - 5^12
Math
kashvisingh9c
Question
Factorise x^12 - 5^12
1 Answer
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1. User Answers tushar0007
x¹² - 5¹²
= (x^6)² - (5^6)²
= (x^6 - 5^6)(x^6 + 5^6)
= [(x³)² - (5³)²](x^6 + 5^6)
= (x³ - 5³)(x³ + 5³)(x^6 + 5^6)
= (x³ - 5³)(x³ + 5³)[(x²)³ - (5²)³]
= (x - 5)(x² + 5x + 5²)(x + 5)(x² - 5x + 5²)[{x² - 5²}{(x²)² + (x²)(5²) + (5²)²}]
= (x - 5)(x² + 5x +25)(x + 5)(x² - 5x + 25)(x - 5)(x + 5)(x⁴ + 25x² + 625).