Cоставьте сумму и разность многочленов и упростите получившиеся выражения: a) 6a^2-3a+1

a) 6a^2 - 3a + 1 + (6a^2 -1) = 6a^2 - 3a + 1 + 6a^2 -1 = 6a^2 + 6a^2 - 3a + 1 - 1 = 12a^2 - 3a = 3a (4a -1),

6a^2 - 3a +1 - (6a^2 -1) = 6a^2 - 3a +1 - 6a^2 +1 = 6a^2 - 6a^2 - 3a +1 +1 =  - 3a + 2.

б) n^3 + 2n^2 - n + 1 + (1 - n^3) = n^3 + 2n^2 - n + 1 + 1 - n^3 = n^3 - n^3 + 2n^2 - n + 1 + 1 = 2n^2 - n + 2 = n (2n -1) +2, 

n^3 + 2n^2 - n + 1 - (1 - n^3) = n^3 + 2n^2 - n + 1 - 1 + n^3 = n^3 + n^3 + 2n^2 - n + 0 = 2n^3 + 2n^2 - n  =n (2n^2 +2n -1).

в) r^3 - 3r^2 + 1 + (2r^3 - 3r^2 + 4) = r^3 - 3r^2 + 1 + 2r^3 - 3r^2 + 4 = r^3 + 2r^3 - 3r^2 - 3r^2 + 1 + 4 =  3r^3 - 6r^2 + 5 =3r^2(r - 2) +5,

r^3 - 3r^2 + 1 - (2r^3 - 3r^2 + 4) =r^3 - 3r^2 + 1 - 2r^3 + 3r^2 - 4 = r^3 - 2r^3 - 3r^2 + 3r^2 + 1 - 4 =  -r^3 - 3. 

г) 3x^2 - 2x + 7 + (2x^2 + 2x + 7) = 3x^2 - 2x + 7 + 2x^2 + 2x + 7 = 3x^2 + 2x^2 - 2x + 2x + 7 + 7 = 5x^2 + 14,

 3x^2 - 2x + 7 - (2x^2 + 2x + 7) = 3x^2 - 2x + 7 - 2x^2 - 2x - 7 = 3x^2 - 2x^2 - 2x - 2x + 7  - 7 = x^2 - 4 x =x(x - 4).