Разложить на множители 1) 1 7/9m^2n^2-1 11/25a^6b^2 2) (3b-5) ^2-49 3) (2x-3) ^2 - (x+4) ^2 4) a^4 - (a-7) ^2 5) (a-b+c) ^2 - (a-b-c) ^2 6) y^4 (x^2+6x+9) - a^8

Формулы: a² - b² = (a - b) (a + b) ;

(a + b) ² = a² + 2ab + b²

1) 1 7/9m²n² - 1 11/25a⁶b² = (4/3mn) ² - (6/5a³b) ² = (1 1/3mn - 1 1/5a³b) (1 1/3mn + 1 1/5a³b)

2) (3b - 5) ² - 49 = (3b - 5) ² - 7² = (3b - 5 - 7) (3b - 5 + 7) = (3b - 12) (3b + 2)

3) (2x - 3) ² - (x + 4) ² = (2x - 3 - (x + 4)) (2x - 3 + (x + 4)) = (2x - 3 - x - 4) (2x - 3 + x + 4) = (x - 7) (3x + 1)

4) a⁴ - (a - 7) ² = (a²) ² - (a - 7) ² = (a² - (a - 7)) (a² + (a - 7)) = (a² - a + 7) (a² + a - 7)

5) (a - b + c) ² - (a - b - c) ² = (a - b + c - (a - b - c)) (a - b + c + (a - b - c)) = (a - b + c - a + b + c) (a - b + c + a - b - c) = 2c (2a - 2b)

6) y⁴ (x² + 6x + 9) - a⁸ = y⁴ (x + 3) ² - a⁸ = (y² (x + 3)) ² - (a⁴) ² = (xy² + 3y² - a⁴) (xy² + 3y² + a⁴)