1) 3mn^2-12m-5n^2+20

2) 9-4x^2-48xy-144y^2

3) xy^3-y^3-8x+8

4) 243x^5-32

Задание разложите на множители

3mn² - 12m - 5n² + 20 = 3m * n² - 3m * 4 - 5 * n² - 5 * (-4) =

= 3m (n² - 4) - 5 (n² - 4) = (3m - 5) (n² - 4) = (3m - 5) (n² - 2²) =

= (3m - 5) (n - 2) (n + 2)

9 - 4x² - 48xy - 144y² = 3² - ((2x) ² - 2*2x * 12y + (12y) ²) =

= 3² - (2x - 12y) ² = - ((2x - 12y) ² - 3²) =

= - (2x - 12y - 3) (2x - 12y + 3)

xy³ - y³ - 8x + 8 = y³ (x - 1) - 8 (x - 1) = (x-1) (y³ - 8) =

= (x - 1) (y³ - 2³) = (x - 1) (y - 2) (y² + y*2 + 2²) =

= (x - 1) (y - 2) (y² + 2y + 4)

243x⁵ - 32 = (3x) ⁵ - 2⁵ = (3x - 2) ((3x) ⁴ + (3x) ³ * 2 + (3x) ² * 2² + 3x * 2³ + 2⁴) =

= (3x - 2) (81x⁴ + 54x³ + 36x² + 24x + 16)