1) ab^2 + a^2b - a^3 - b^3 = b^2*(a - b) + a^2(b - a) = (a - b)(b^2 - a^2) =
= -(a - b)(a^2 - b^2) = -(a - b)(a - b)(a + b) = -(a + b)(a - b)^2
2) -3x^2 + 48 = -3(x^2 - 16) = -3(x - 4)(x + 4)
3) Здесь, возможно, опечатка, должно быть a^3, тогда это разность кубов.
a^3 - 8b^3 = (a - 2b)(a^2 + 2ab + 4b^2)
4) ![\frac{20mn-4m^2}{m^2-10mn+25n^2} = \frac{4m(5n-m)}{(5n-m)^2} = \frac{4m}{5n-m} \frac{20mn-4m^2}{m^2-10mn+25n^2} = \frac{4m(5n-m)}{(5n-m)^2} = \frac{4m}{5n-m}](https://tex.z-dn.net/?f=+%5Cfrac%7B20mn-4m%5E2%7D%7Bm%5E2-10mn%2B25n%5E2%7D+%3D+%5Cfrac%7B4m%285n-m%29%7D%7B%285n-m%29%5E2%7D+%3D+%5Cfrac%7B4m%7D%7B5n-m%7D+)