數學10條...thx!!!

1)a⁴- b⁴
= (a²)² - (b²)²
= (a² - b²) (a² + b²)
= (a - b) (a + b) (a² + b²)

2) 16a⁴- 81
= (4a²)² - 9²
= (4a² - 9) (4a² + 9)
= (2a - 3) (2a + 3) (4a² + 9)

3)(2a - b)² - (2a + b)²
= [(2a - b) - (2a + b)] [(2a - b) + (2a + b)]
= (- 2b) (4a)
= - 8abor(2a - b)² - (2a + b)²
= (4a² - 2(2a)(b) + b²) - (4a² + 2(2a)(b) + b²)
= - 2(2a)(b) - 2(2a)(b)
= - 4ab - 4ab
= - 8ab

4) a⁶ - a²
= a² (a⁴- 1)
= a² (a² - 1)(a² + 1)
= a² (a - 1) (a + 1) (a² + 1)ora⁶ - a²
= (a³)² - a²
= (a³ - a) (a³ + a)
= a(a² - 1) a(a² + 1)
= a(a - 1)(a + 1) a(a² + 1)
= a² (a - 1) (a + 1) (a² + 1)
5)1 - 4a² b⁴
= 1 - (2ab²)²
= (1 - 2ab²) (1 + 2ab²)

6) x² - 4m²n²
= x² - (2mn)²
= (x - 2mn) (x + 2mn)

7)(x + 4)² - 36
= (x + 4)² - 6²
= (x + 4 - 6) (x + 4 + 6)
= (x - 2) (x + 10)

8) x⁸ - 16
= ( x⁴)² - 4²
= (x⁴- 4) (x⁴+ 4)
= (x² - 2)(x² + 2) (x⁴+ 4) ........ (to 3 factors)
Further more :
= (x² - 2)(x² + 2) ( x⁴+ 2(x²)(2) + 4 - 2(x²)(2) )
= (x² - 2)(x² + 2) ( (x² + 2)² - (2x)² )
= (x² - 2)(x² + 2) (x² - 2x + 2)(x² + 2x + 2)

9) 4(x + y)² - 9
= (2(x + y))² - 3²
= (2(x + y) - 3) (2(x + y) + 3)
= (2x + 2y - 3) (2x + 2y + 3)

10) (x + y)² - (m - n)²
= [(x + y) - (m - n)] [(x + y) + (m - n)]
= (x + y - m + n) (x + y + m - n)