Как разложить на множетели: 3x^2-12 32a^4b-2a^2b 2m^2+2n^2-4mn 12m^5n+24m^4n+12m^3n (x^2+2x) ^2-1 81 - (y^2+6y) ^2

1) 3x^2 - 12 = 3 (x^2 - 4) = 3 (x - 2) (x + 2);

2) 32a^4b - 2a^2b = 2a^2b (16a^2 - 1) = 2a^2b (4a - 1) (4a + 1);

3) 2m^2 + 2n^2 - 4mn = 2 (m^2 + n^2 - 2mn) = 2 (m - n) ^2;

4) 12m^5n + 24m^4n + 12m^3n = 12m^3n (m^2 + 2m + 1) = 12m^3n (m + 1) ^2;

5) (x^2 + 2x) ^2 - 1 = (x^2 + 2x - 1) (x^2 + 2x + 1);

6) 81 - (y^2 + 6y) ^2 = (9 - (y^2 + 6y)) (9 + y^2 + 6y) = (9 - y^2 - 6y) (y + 3) ^2.

Ответы: 1) 3 (x - 2) (x + 2);

2) 2a^2b (4a - 1) (4a + 1);

3) 2 (m - n) ^2;

4) 12m^3n (m + 1) ^2;

5) (x^2 + 2x - 1) (x^2 + 2x + 1);

6) (9 - y^2 - 6y) (y + 3) ^2.