Разложить на множители 1) 16 - 9a^2 - 72ab - 144b^2 2) ac^3 + c^3 - 27a - 27 3) 32 + 243x^5

1)

16 - 9 а² - 72ab - 144b² =

= - ((3a) ² + 2*3a*12b + (12b) ² - 4²) =

= - ((3a + 12b) ² - 4²) =

= - (3a + 12b - 4) (3a + 12b + 4)

2)

ac³+c³ - 27a - 27 =

= c³ (a + 1) - 27 (a + 1) =

= (a + 1) (c³ - 27) =

= (a + 1) (c³ - 3³) =

= (a + 1) (c - 3) (c² + 3c + 3²) =

= (a + 1) (c - 3) (c² + 3c + 9)

3)

32 + 243a⁵ = (3a) ⁵ + 2⁵ =

= (3a + 2) ((3a) ⁴ - (3a) ³ * 2 + (3a) ² * 2² - 3a * 2³ + 2⁴)

= (3a + 2) (81a⁴ - 27a³ * 2 + 9a² * 4 - 3a * 8 + 16)

= (3a + 2) (81a⁴ - 54a³ + 36a² - 24a + 16)