Simplify (3a-4)b+2: Applying the Distributive Property

We begin by opening the parentheses using the distributive property in order to simplify the expression:

$x(y+z)=xy+xz$Note that in the distributive property formula we assume that there is addition between the terms inside of the parentheses, therefore it is crucial to take into account the sign of the coefficient of the term.

Furthermore, we apply the rules of multiplication of signs in order to present any expression within the parentheses. The parentheses are opened with the help of the distributive property, as an expression in which there is an addition operation between all the terms:

$(3a-4)b+2\\ \big(3a+(-4)\big)b+2$We continue and open the parentheses using the distributive property:

$\big(3a+(-4)\big)b+2\\ 3a\cdot b+(-4)\cdot b +2\\ 3ab-4b+2$Therefore, the correct answer is option c.