Evaluate the binomial squared first by order of operations.

$\displaystyle (x-6)^2 = (x-6)(x-6)$

$\displaystyle = x(x)+(x)(-6)+(-6)(x)+(-6)(-6)$

$\displaystyle x^2-12x+36$

The expression becomes:

$\displaystyle -6(x^2-12x+36)-3x+2$

Distribute the negative six through each term of the trinomial.

$\displaystyle -6x^2+72x-216-3x+2$

Combine like-terms.

The answer is:  $\displaystyle -6x^2+69x-214$

Substitute the value of $\displaystyle a$ into the given expression.

$\displaystyle 6(3)((3)^2-(3)^3)$

Simplify the parentheses by order of operations. 

$\displaystyle 18(9-27) = 18(-18) = -324$

The answer is:  $\displaystyle -324$

Substitute the assigned values into the expression.

$\displaystyle \frac{1}{b}-\frac{b}{a} = \frac{1}{6}-\frac{6}{5}$

Convert the fractions to a common denominator.

$\displaystyle \frac{1}{6}-\frac{6}{5} = \frac{1(5)}{6(5)}-\frac{6(6)}{5(6)} = \frac{5}{30}- \frac{36}{30}$

Now that the denominators are common, the numerators can be subtracted.

The answer is:  $\displaystyle -\frac{31}{30}$

Substitute the values into the expression.

$\displaystyle a(2-b)-a = 4(2-6)-4$

Simplify the expression by distribution.

$\displaystyle 4(2-6)-4 = 4(-4)-4 = -16-4 = -20$

The answer is:  $\displaystyle -20$

Substitute the values of $\displaystyle a$ and $\displaystyle b$.

$\displaystyle \frac{15}{\sqrt{5}\cdot \sqrt{3}} = \frac{15}{\sqrt{15}}$

Rationalize the denominator by multiplying the top and bottom with the denominator.  This will eliminate the radical in the denominator.

$\displaystyle \frac{15}{\sqrt{15}}\cdot \frac{\sqrt{15}}{\sqrt{15}}=\frac{15\sqrt{15}}{15}$

Cancel the integers.

The answer is:  $\displaystyle \sqrt{15}$

In order to solve this expression, we will need to substitute the assigned values into $\displaystyle a$ and $\displaystyle b$.

$\displaystyle 3a^2-9b^3 = 3(6)^2-9(2)^3$

Simplify the terms by order of operation.

$\displaystyle 3(6)^2-9(2)^3 = 3(36)-9(8) = 108-72=36$

The answer is:  $\displaystyle 36$

Substitute the values into the expression.

$\displaystyle 2a^2-4b^3 = 2(5)^2-4(-3)^3$

Simplify the terms by order of operations.

$\displaystyle 2(5)^2-4(-3)^3 = 2(25) - 4(-27)$

$\displaystyle =50 + 108=158$

The answer is:  $\displaystyle 158$

Substitute the values into the expression.

$\displaystyle -(6)^{-2}-(-6)^{-2}$

In order to evaluate this expression, we will need to rewrite the negative exponents into fractions.

$\displaystyle -(6)^{-2}-(-6)^{-2}= -\frac{1}{6^2}-\frac{1}{(-6)^2}$

Simplify the fractions.

$\displaystyle -\frac{1}{36}-\frac{1}{36} =- \frac{2}{36}$

Reduce this fraction.  

The answer is:  $\displaystyle -\frac{1}{18}$

Substitute the values in the expression.

$\displaystyle \frac{b}{\sqrt a} = \frac{2}{\sqrt 3}$

Rationalize the denominator by multiplying square root of three on the top and bottom of the fraction.

$\displaystyle \frac{2}{\sqrt 3}\cdot \frac{\sqrt 3}{\sqrt 3}$

Simplify the top and bottom.

The answer is:  $\displaystyle \frac{2\sqrt{3}}{3}$