Разложите на множители:

(a-x) (х^3-y^3) - (x-y) (a^3-x^3)

2x^3-2xy^2-6x^2+6y^2

5a^2-5b^2-10a^3b+10ab^3

36x^3-144x-36x^2+144

y^3+ay^2-b^2y-b^2a

(a-x) (x³-y³) - (x-y) (a³-x³) =

= (a-x) (x-y) (x²+xy+y²) - (x-y) (a-x) (a²+ax+x²) =

= (a-x) (x-y) (x²+xy+y²-a²-ax-x²) =

= (a-x) (x-y) (y²-a²+xy-ax)

2x³-2xy²-6x²+6y²=

= (2x³-2xy²) - (6x²-6y²) =

=2x (x²-y²) - 6 (x²-y²) =

= (x²-y²) (2x-6) =

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

5a²-5b²-10a³b+10ab³=

= (5a²-5b²) - (10a³b-10ab³) =

=5 (a²-b²) - 10ab (a²-b²) =

= (a²-b²) (5-10ab) =

=5 (1-5ab) (a-b) (a+b)

36x³-144x-36x²+144=

= (36x³-36x²) - (144x-144) =

=36x² (x-1) - 144 (x-1) =

= (x-1) (36x²-144) =

= (x-1) (6x-12) (6x+12) =

= (x-1) * 6 (x-2) * 6 (x+2) =

=36 (x-1) (x-2) (x+2)

y³+ay²-b²y-b²a=

= (y³+ay²) - (b²y+b²a) =

=y² (y+a) - b² (y+a) =

= (y+a) (y²-b²) =

= (y+a) (y-b) (y+b)