404. a) 2a² + 3a-4+ (5a²-a + 7); 6) 6x³+8x-5-(4x² + 8x - 5); B) 324-223 2z3+122-5-(324 + 122 - 5 - (324 - 2z-5); г) -5c3-2c+3c2-(1-c-2c²-4c³); г) (2x + y) + (3x-4y) - (5x + 3y - 1); д) 8ас - (За² - 2с² + 2ac) - (4a² + 2c²).

Решение

а) $$2a^2 + 3a - 4 + (5a^2 - a + 7) = 2a^2 + 3a - 4 + 5a^2 - a + 7 = (2a^2 + 5a^2) + (3a - a) + (-4 + 7) = 7a^2 + 2a + 3$$.

б) $$6x^3 + 8x - 5 - (4x^2 + 8x - 5) = 6x^3 + 8x - 5 - 4x^2 - 8x + 5 = 6x^3 - 4x^2 + (8x - 8x) + (-5 + 5) = 6x^3 - 4x^2$$.

в) $$3z^4 - 2z^3 + 12z - 5 - (3z^4 - 2z - 5) = 3z^4 - 2z^3 + 12z - 5 - 3z^4 + 2z + 5 = (3z^4 - 3z^4) - 2z^3 + (12z + 2z) + (-5 + 5) = -2z^3 + 14z$$.

г) $$-5c^3 - 2c + 3c^2 - (1 - c - 2c^2 - 4c^3) = -5c^3 - 2c + 3c^2 - 1 + c + 2c^2 + 4c^3 = (-5c^3 + 4c^3) + (3c^2 + 2c^2) + (-2c + c) - 1 = -c^3 + 5c^2 - c - 1$$.

д) $$(2x + y) + (3x - 4y) - (5x + 3y - 1) = 2x + y + 3x - 4y - 5x - 3y + 1 = (2x + 3x - 5x) + (y - 4y - 3y) + 1 = 0 - 6y + 1 = -6y + 1$$.

е) $$8ac - (3a^2 - 2c^2 + 2ac) - (4a^2 + 2c^2) = 8ac - 3a^2 + 2c^2 - 2ac - 4a^2 - 2c^2 = (-3a^2 - 4a^2) + (2c^2 - 2c^2) + (8ac - 2ac) = -7a^2 + 0 + 6ac = 6ac - 7a^2$$.

Ответ: а) $$7a^2 + 2a + 3$$; б) $$6x^3 - 4x^2$$; в) $$-2z^3 + 14z$$; г) $$-c^3 + 5c^2 - c - 1$$; д) $$-6y + 1$$; е) $$6ac - 7a^2$$.