Expanding (x + 2)(x - 3) gives x^2 - 3x + 2x - 6 = x^2 - x - 6.

Using the power of a product rule, (x^3 * y^2)^2 = x^(3*2) * y^(2*2) = x^6 * y^4.

Distributing 2 gives 2x + 6, and then subtracting 4 results in 2x + 2.

Distributing 2 gives 2 * x + 2 * 3 = 2x + 6.

Distributing gives 3x + 12 - 2x + 2 = x + 14.

Distributing 3 gives 3x + 12, which is the equivalent expression.

Using the property of exponents that states a^m * a^n = a^(m+n), we combine the exponents: 2x + (x + 1) = 3x + 1.

log_10(0.01) can be rewritten as log_10(10^-2) = -2.

log_10(1/100) = log_10(10^-2) = -2.

log_10(100) = 2 and log_10(10) = 1, so 2 + 1 = 3.

Since 1000 is 10^3, log_10(1000) = 3.

Using the property of logarithms, log_5(25) = 2 and log_5(5) = 1. Therefore, log_5(25) + log_5(5) = 2 + 1 = 3, which is log_5(125).

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

Both 1/4^x and 4^(-x) represent the inverse of 4^x.

The product (x + 1)(x - 1) is a difference of squares, resulting in x^2 - 1.

The product of the roots of a quadratic polynomial ax^2 + bx + c is given by c/a. Here, c = 4 and a = 1, so the product is 4.

To find the sum of the coefficients, substitute x = 1 into the expression: (2(1) - 3)^4 = (-1)^4 = 1, but the coefficients sum to -81.

The sum of the roots is given by -b/a, which is -3/5 for this equation.

The vertex of the quadratic equation is given by the point (-b/2a, f(-b/2a)).

Plutonium is widely used in nuclear reactors and weapons due to its fissile properties.

Neodymium is used in making strong permanent magnets, known as neodymium magnets.

Uranium is commonly used as fuel in nuclear reactors.

Uranium is commonly used in the production of nuclear reactors due to its fissile properties.

The British colonial policies, particularly in agriculture, led to widespread poverty due to exploitative land revenue systems and neglect of rural development.

The weakness of the Delhi Sultanate allowed the Mughals to establish their dominance, as they capitalized on the discontent among the local rulers and the fragmented political landscape.

All of the above factors contributed to the agricultural decline in the Roman Empire, including overreliance on slave labor, technological stagnation, and climate change.

The nature of the solvent does not directly affect Gibbs Free Energy; it is primarily influenced by temperature, pressure, and concentration.

Density does not directly affect surface tension; it is influenced by temperature, impurities, and the nature of the liquid.

The color of the wire does not affect the accuracy of a potentiometer; however, temperature, length, and material do.

The color of the adsorbent does not affect its adsorption capacity; factors like surface area, temperature, and nature of the adsorbate do.