Expand the Expression: (2x+3)(-5-x) Using Distributive Property

Let's simplify the given expression and open the parentheses using the extended distribution law:

$(\textcolor{red}{a}+\textcolor{blue}{b})(c+d)=\textcolor{red}{a}c+\textcolor{red}{a}d+\textcolor{blue}{b}c+\textcolor{blue}{b}d$

Note that in the formula template for the above distribution law, we take by default that the operation between the terms inside the parentheses is addition.

Therefore the sign preceding the term is an inseparable part of it. We'll also apply the rules of sign multiplication and thus we can present any expression in parentheses, which we'll open using the above formula, first as an expression where addition operation exists between all terms:

$(2x+3)(-5-x)\\ (\textcolor{red}{2x}+\textcolor{blue}{3})((-5)+(-x))\\$Let's begin by opening the parentheses:

$(\textcolor{red}{2x}+\textcolor{blue}{3})((-5)+(-x))\\ \textcolor{red}{2x}\cdot (-5)+\textcolor{red}{2x}\cdot(-x)+\textcolor{blue}{3}\cdot (-5) +\textcolor{blue}{3} \cdot(-x)\\ -10x-2x^2-15-3x$

In calculating the above multiplications, we used the multiplication table and the laws of exponents for multiplication between terms with identical bases:

$a^m\cdot a^n=a^{m+n}$

In the next step we'll combine like terms. Like terms are terms where the variable (or variables each separately), in this case x, have identical exponents. In the absence of one of the variables from the expression, we'll consider its exponent as zero power, due to the fact that raising any number to the power of zero yields the result 1) We'll apply the commutative law of addition, additionally we'll arrange the expression from highest to lowest power from left to right (we'll treat the free number as having zero power):
$\textcolor{purple}{-10x}\textcolor{green}{-2x^2}-15\textcolor{purple}{-3x}\\ \textcolor{green}{-2x^2} \textcolor{purple}{-10x}\textcolor{purple}{-3x}-15\\ \textcolor{green}{-2x^2}\textcolor{purple}{-13x}-15$

In the combining of like terms performed above, we highlighted the different terms using colors, and as emphasized before, we made sure that the sign preceding the term remains an inseparable part of it,

We therefore got that the correct answer is answer D.