The coefficient of x^0 is C(3,0) * 5^3 = 1 * 125 = 125.

The coefficient of x^0 is C(5,0) * 5^5 = 1 * 3125 = 3125.

Using the binomial theorem, the coefficient of x^2 in (a + b)^n is given by nCk * a^(n-k) * b^k. Here, n=6, a=x, b=-4, and k=2. Thus, the coefficient is 6C2 * (1)^4 * (-4)^2 = 15 * 16 = 240.

Using the binomial theorem, the coefficient of x^3 is given by C(5,3) * (2)^3 * (3)^(5-3) = 10 * 8 * 9 = 720.

The coefficient of x^4 is C(6,4) * (2)^4 * (3)^(6-4) = 15 * 16 * 9 = 2160.

The coefficient of x^4 is C(5, 4) * (2)^4 * (-3)^1 = 5 * 16 * (-3) = -240.

The coefficient of x^4 is C(6,4) = 15.

The coefficient of x^5 is C(10,5) * (1/2)^5 = 252 * 1/32 = 7.875.

The coefficient of x^5 is C(7,5)(2)^2 = 21 * 4 = 84.

The coefficient of x^5 is C(8,5) * (2)^3 = 56 * 8 = 448.

Using the binomial theorem, the coefficient of x^5 in (x + 3)^8 is given by 8C5 * (3)^3 = 56 * 27 = 1512.

The coefficient of x^6 is C(8,6) * (5)^2 = 28 * 25 = 700.

The complex ion [Cu(H2O)6]2+ is blue due to d-d transitions.

[Cu(H2O)6]2+ is known to exhibit a blue color due to d-d transitions in the presence of water ligands.

The combined gas law is represented by the equation P1V1/T1 = P2V2/T2, which combines Boyle's, Charles's, and Gay-Lussac's laws.

The common oxidation state of actinides in their compounds is +4.

Alkali metals have a common oxidation state of +1.

Chromium commonly exhibits a +6 oxidation state in chromates (CrO4^2-).

In Cr2O7^2-, chromium has a common oxidation state of +6.

Chromium commonly exhibits a +6 oxidation state in compounds such as chromium trioxide (CrO3).

Group 17 elements, also known as halogens, commonly exhibit an oxidation state of -1.

In ammonia, nitrogen has an oxidation state of -3.

The common oxidation state of group 13 elements, such as Aluminum, is +3.

Transition metals commonly exhibit a +2 oxidation state due to the loss of two 4s electrons.

The common ratio r = 12/4 = 3.

f(g(x)) = f(2x) = 2x + 1.

Mass of KCl = 0.5 moles × 74.5 g/mol = 37.25 g. Concentration = 37.25 g / 1.5 L = 24.83 g/L.

Molality (m) = moles of solute / kg of solvent = 5 moles / 3 kg = 1.67 m.

Molarity (M) = moles of solute / liters of solution = 0.5 moles / 1.5 L = 0.33 M.

PPM = (mass of solute in grams / volume of solution in liters) * 10^6 = (1 g / 1 L) * 10^6 = 1000 ppm.