357. Упростите выражение: 1) 8x-2x(3x + 4); 2) 7a²+3a(9-5а); 3) 6x(4x-7)-12(2x² + 1); 4) c (c²-1) + c²(c-1); 5) 2m(m-3n) + m(5m + 11n); 6) 8x(x²+y²)-9x (x² - y²); 7) 5b³ (2b-3)-2,5b³ (4b-6); 8) x (5x²+6x+8) - 4x (2+2x+x²).

Решение:

1. \[ 8x - 2x(3x + 4) = 8x - 6x^2 - 8x = -6x^2 \]
2. \[ 7a^2 + 3a(9 - 5a) = 7a^2 + 27a - 15a^2 = -8a^2 + 27a \]
3. \[ 6x(4x - 7) - 12(2x^2 + 1) = 24x^2 - 42x - 24x^2 - 12 = -42x - 12 \]
4. \[ c(c^2 - 1) + c^2(c - 1) = c^3 - c + c^3 - c^2 = 2c^3 - c^2 - c \]
5. \[ 2m(m - 3n) + m(5m + 11n) = 2m^2 - 6mn + 5m^2 + 11mn = 7m^2 + 5mn \]
6. \[ 8x(x^2 + y^2) - 9x(x^2 - y^2) = 8x^3 + 8xy^2 - 9x^3 + 9xy^2 = -x^3 + 17xy^2 \]
7. \[ 5b^3(2b - 3) - 2.5b^3(4b - 6) = 10b^4 - 15b^3 - 10b^4 + 15b^3 = 0 \]
8. \[ x(5x^2 + 6x + 8) - 4x(2 + 2x + x^2) = 5x^3 + 6x^2 + 8x - 8x - 8x^2 - 4x^3 = x^3 - 2x^2 \]