Разложите на множители:

а) 18a^2-2

б) 2ax^3-16ay^3

в) 4a^4y-8a^2by+4b^2y

г) 9m^2-6m-10p-25p^2

д) 9x^2+9ax^2-y^2+ay^2+6axy

А) 18a^2-2=2 (9a²-1) = 2 (3a-1) (3a+1)

б) 2ax^3-16ay^3=2a (x³-8y³) = 2a (x-2y) (x²+2xy+4y²)

в) 4a^4y-8a^2by+4b^2y=4 (a⁴y-2a²by+b²y) =

4 (a⁴y-a²by-a²by+b²y) = 4 ((a⁴y-a²by) + (b²y-a²by)) =

4 ((a²y (a²-b) + by (b-a²)) = 4 ((a²y (a²-b) - by (a²-b)) =

4 (a²-b) (a²y-by) = 4y (a²-b) (a²-b) = 4y (a²-b) ²

г) 9m^2-6m-10p-25p^2 = (9m²-25p²) - (6m+10p) =

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

д) 9x^2+9ax^2-y^2+ay^2+6axy=

(9x²-y²) + (9ax²+6axy+ay²) = (3x-y) (3x+y) + a (9x²+6xy+y²) = (3x-y) (3x+y) + a (3x+y) ²=

(3x+y) (3x-y+a (3x+y)) = (3x+y) (3x-y+3ax+ay)