Factorize x2 - 1, write 5x5x5x5x5 using indices, and simplify 3b2/2b2.

In $x^2 - 1$, we have $a^2 = x^2 \implies a = x$ and $b^2 = 1 \implies b = 1$.

The completely factorized expression is $\boxed{(x-1)(x+1)}$.

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To write $5 \times 5 \times 5 \times 5 \times 5$ using indices, we count how many times the base number 5 is multiplied by itself.

The base number is 5.

The number 5 is multiplied by itself 5 times.

The expression in index notation is $\boxed{5^5}$.

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To simplify the expression $\frac{3b^2}{2b^2}$ using laws of indices, we can cancel out common terms.

Both the numerator and the denominator have $b^2$.

Alternatively, using the law of indices $\frac{a^m}{a^n} = a^{m-n}$:

Since any non-zero number raised to the power of 0 is 1 ($b^0 = 1$):

The simplified expression is $\boxed{\frac{3}{2}}$.

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To factorize the expression $4x^2 + 4x$, we find the greatest common factor (GCF) of the terms and factor it out.

The terms are $4x^2$ and $4x$.

The numerical coefficients are 4 and 4, so the common numerical factor is 4.
The variable parts are $x^2$ and $x$, so the common variable factor is $x$.
The GCF is $4x$.

The factorized expression is $\boxed{4x(x+1)}$.

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To expand the expression $(3x+2)(x-4)$, we use the FOIL method (First, Outer, Inner, Last).

The expanded expression is $\boxed{3x^2 - 10x - 8}$.