Question

factorise:
1) s^12 - t^12
2)1-p^8​

Answer 1

Answer:

1) s¹² - t¹²

=> (s² + t²)(s⁴ - s²t² + t⁴)(s + t)(s² - st + t²)

2) 1 - p^8

=> (1 + p⁴)(1 + p²)(1 + p)(1 - p)

Answer 2

AnswEr :

1 ] s¹² - t¹²

➟ (s⁶)² - (t⁶)²

▣ [ a² - b² = (a - b)(a + b) ]

➟ (s⁶ - t⁶)(s⁶ + t⁶)

➟ ((s³)² - (t³)²)(s⁶ + t⁶)

➟ (s³ - t³)(s³ + t³)(s⁶ + t⁶)

▣ [ a³ - b³ = (a - b)(a² + ab + b²) ]

▣ [ a³ + b³ = (a + b)(a² - ab + b²) ]

➟ (s - t)(s + t)(s² + st + t²)(s² - st + t²)(s⁶ + t⁶)

━━━━━━━━━━━━━━━━━━━━━━━━

2 ] 1 - p⁸

➟ (1⁴)² - (p⁴)²

▣ [ a² - b² = (a - b)(a + b) ]

➟ (1 + p⁴)(1 - p⁴)

➟ (1 + p⁴)((1²)² - (p²)²)

➟ (1 + p⁴)(1 + p²)(1 - p²)