Question

Разложить на множители 1) 1 79m^2n^2-1 1125a^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

Answer 1

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)