Разложите ** множителиw^18+4w^9+4-100w^8​

Question

Разложите на множителиw^18+4w^9+4-100w^8​

Answer 1

(a + b)² = a² + 2ab + b²

a² - b² = (a - b)(a + b)

w¹⁸ + 4w⁹ + 4 - 100w⁸ = (w⁹)² + 2*2*w⁹ + 2² - (10w⁴)² = (w⁹ + 2)² - (10w⁴)² = (w⁹ + 10w⁴ + 2)(w⁹ - 10w⁴ + 2)