Приведите к многочлену стандартного вида: 1) (x-3) ^2-x (x+9) 2) (2a+5) ^2-5 (4a+5) 3) (a-3) (a+3) + a (a+4) 4) (4x+5y) ^2 - (4x-5y) ^2 5) (b+7c) ^2 - (7c-b) ^2

1) (x - 3) ^2 - x (x + 9) = x^2 - 2 * x * 3 + 3^2 - x * x - x * 9 = x^2 - 6x + 9 - x^2 - 9x;

Приводим подобные:

x^2 - x^2 - 6x - 9x + 9 = - 15x + 9;

2) (2a + 5) ^2 - 5 (4a + 5) = 4a^2 + 20a + 25 - 20a - 25 = 4a^2 + 20a - 20a + 25 - 25 = 4a^2;

3) (a - 3) (a + 3) + a (a + 4) = a^2 - 3^2 + a * a + a * 4 = a^2 - 9 + a^2 + 4a = a^2 + a^2 + 4a - 9 = 2a^2 + 4a - 9;

4) (4x + 5y) ^2 - (4x - 5y) ^2 = 16x^2 + 40xy + 25y^2 - (16x^2 - 40xy + 25y^2) = 16x^2 - 16x^2 + 40xy + 40xy + 25y^2 - 25y^2 = 80xy;

5) (b + 7c) ^2 - (7c - b) ^2 = b^2 + 14bc + 49c^2 - 49c^2 + 14bc - b^2 = 28bc.