93. Преобразуйте в многочлен стандартного вида выражение:
1) $$2.4(5x - 10) - 5(x + 1) - 3(1 - 3x);$$ $$12x - 24 - 5x - 5 - 3 + 9x = (12x - 5x + 9x) + (-24 - 5 - 3) = 16x - 32$$
Ответ: $$16x - 32$$
2) $$-2x(x + 4) + 5(x^2 - 3x);$$ $$-2x^2 - 8x + 5x^2 - 15x = (-2x^2 + 5x^2) + (-8x - 15x) = 3x^2 - 23x$$
Ответ: $$3x^2 - 23x$$
3) $$3a(3a - a^2) - 4a(2a^2 - 5a);$$ $$9a^2 - 3a^3 - 8a^3 + 20a^2 = (-3a^3 - 8a^3) + (9a^2 + 20a^2) = -11a^3 + 29a^2$$
Ответ: $$-11a^3 + 29a^2$$
4) $$3m(n - 2m) - m(m + 4n);$$ $$3mn - 6m^2 - m^2 - 4mn = (3mn - 4mn) + (-6m^2 - m^2) = -mn - 7m^2$$
Ответ: $$-mn - 7m^2$$
5) $$0.3x^2(x^2 - 3x + 2) - 0.6x(2x^3 + 6x^2 - 4x);$$ $$0.3x^4 - 0.9x^3 + 0.6x^2 - 1.2x^4 - 3.6x^3 + 2.4x^2 = (0.3x^4 - 1.2x^4) + (-0.9x^3 - 3.6x^3) + (0.6x^2 + 2.4x^2) = -0.9x^4 - 4.5x^3 + 3x^2$$
Ответ: $$-0.9x^4 - 4.5x^3 + 3x^2$$
6) $$4x(7y - 3x^2) - 3y(x - y^2);$$ $$28xy - 12x^3 - 3xy + 3y^3 = -12x^3 + 3y^3 + (28xy - 3xy) = -12x^3 + 3y^3 + 25xy$$
Ответ: $$-12x^3 + 3y^3 + 25xy$$
7) $$5a(3a - 2b) + 17b(2a + b) - 3a(-4b + a);$$ $$15a^2 - 10ab + 34ab + 17b^2 + 12ab - 3a^2 = (15a^2 - 3a^2) + 17b^2 + (-10ab + 34ab + 12ab) = 12a^2 + 17b^2 + 36ab$$
Ответ: $$12a^2 + 17b^2 + 36ab$$
8) $$2x^3(3x - 1) - 4x(x^3 - 2x^2 + 3x) - x(5 + 2x^3);$$ $$6x^4 - 2x^3 - 4x^4 + 8x^3 - 12x^2 - 5x - 2x^4 = (6x^4 - 4x^4 - 2x^4) + (-2x^3 + 8x^3) - 12x^2 - 5x = 6x^3 - 12x^2 - 5x$$
Ответ: $$6x^3 - 12x^2 - 5x$$