Expand (x+7)(x-9): Find the Missing Coefficient in x²+□x-63

Let's simplify the expression given on the left side:

$(x+7)(x-9)$

Let's open the parentheses using the expanded 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 distribution law mentioned, we take by default that the operation between terms inside the parentheses is addition, so we won't forget of course that the sign preceding the term is an integral part of it, and 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 occurs between all terms (if needed),

Therefore, we'll first present each of the expressions in parentheses in the multiplication on the left side as an expression containing addition:

$(x+7)(x-9)=x^2+\textcolor{purple}{\boxed{?}}x-63 \\ \downarrow\\ \big(x+(+7)\big)\big(x+(-9)\big)=x^2+\textcolor{purple}{\boxed{?}}x-63 \\$Now for convenience, let's write again the expanded distribution law mentioned earlier:

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

And apply it to our problem:

$\big (\textcolor{red}{x}+\textcolor{blue}{(+7)}\big)\big(x+(-9)\big)=x^2+\textcolor{purple}{\boxed{?}}x-63 \\ \downarrow\\ \textcolor{red}{x}\cdot x +\textcolor{red}{x}\cdot (-9)+\textcolor{blue}{(+7)}\cdot x +\textcolor{blue}{(+7)}\cdot (-9)=x^2+\textcolor{purple}{\boxed{?}}x-63 \\$We'll continue and apply the multiplication sign rules, remember that multiplying terms with identical signs yields a positive result, and multiplying terms with different signs yields a negative result, in the next step we'll combine like terms in the expression obtained on the left side:

$\textcolor{red}{x}\cdot x +\textcolor{red}{x}\cdot (-9)+\textcolor{blue}{(+7)}\cdot x +\textcolor{blue}{(+7)}\cdot (-9)=x^2+\textcolor{purple}{\boxed{?}}x-63 \\ \downarrow\\ x^2-9x+7x-63=x^2+\textcolor{purple}{\boxed{?}}x-63 \\ x^2-2x-63=x^2+\textcolor{purple}{\boxed{?}}x-63$

Therefore the missing expression is the number $-2$,

That is - the correct answer is a'.