1)Выделите квадрат двучлена: a+6a-10; x-4x+1; c+10c; x+3x-0,25; a-1/4a+1/4; 2)Обоснуйте равенство: (1-а)+2а(1-а)+а=1;

1)a^2 + 6a 10 = a^2 +2 * 3a + 9 9 10 = (a + 3)^2 -19.

x^2 4x + 1 = x^2 2 * 2 * 2x + 4 4 + 1 = (x 2)^2 3.

c^2 + 10c = c^2 + 2 * 5c + 25 -25 = (c + 5)^2 25.

x^2 + 3x 0.25 = x^2 + 2 * 1/2 * 3x + 1/4 1/4 0.25 = (x +1/2)^2 0.6 .

a^2 1/4 * a + 1/4  = a^2 2 * 1/2 * 1/4 * a + 1/16 1/16 + 1/4 = (a 1/4 )^2 1/16 + 4/16 = (a 1/4)^2  + 3/16.

2)(1 a)^2 + 2a(1 a) + a^2 = 1,

1 2a + a^2 + 2a 2a^2 + a^2 = 1.

(x + y)^2 2(x + y)(x y) + (x y)^2 = x^2 + 2xy + y^2 2(x^2 y^2) + x^2 2xy + y^2 = 2x^2 + 2y^2 2x^2 + 2y^2 = 4y^2.

3)a^2 + 3ab + b^2 = a^2 + 2 * 1/2 *3ab + (3/2 * b)^2  - (3/2 * b)^2  + b^2 = (a + 3/2 * b)^2 9/4 *b ^2 + b^2 = (a + 3/2)^2 5/4 * b^2.

x^2 + xy + y^2 = x^2 + 2 * 1/2 * xy + (1/2 * y)^2 (1/2 *y)^2 + y^2 = (x+1/2 *y)^2 1/4 * y^2 + y^2 = (x + 1/2 * y)^2 + 3/4 * y^2.

m^2 mn + n^2 = m^2 2 * 1/2 * mn + (1/2 * n) ^ 2 (1/2 * n)^2  + n^2 = (m 1/2)^2  - 1/4 * n^2 + n^2 = (m 1/2 * n)^2 + 3/4 *n^2.

4a^2 +5ac + c^2 = 4a^2 + 2 * 1/2 * 2/2 * 5ac + (5/4 * c)^2 (5/4 *c)^2 + c^2 = (2a + 5/4*c)^2 25/16 *c^2 + c^2 = (2a + 5/4 *c)^2  - 9/16 *c^2.