Expanding (x+7)(x-2): Find the Missing Term in Quadratic Expression

Complete the following equation:

_{$(x+7)(x-2)=x^2+\textcolor{red}{☐}x-14$}

Simplify the given expression on the left side:

$(x+7)(x-2)$ Open the parentheses by 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, the operation between terms inside the parentheses is automatically addition. Likewise remember that the sign preceding the term is an integral part of it. Proceed to apply the rules of sign multiplication allowing us to present any expression inside of parentheses. The parentheses can be opened using the above formula, first, as an expression where addition operation exists between all terms (if needed),

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

$(x+7)(x-2)=x^2+\textcolor{purple}{\boxed{?}}x-14 \\ \downarrow\\ \big(x+(+7)\big)\big(x+(-2)\big)=x^2+\textcolor{purple}{\boxed{?}}x-14 \\$Let's once again write 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:

$\big (\textcolor{red}{x}+\textcolor{blue}{(+7)}\big)\big(x+(-2)\big)=x^2+\textcolor{purple}{\boxed{?}}x-14 \\ \downarrow\\ \textcolor{red}{x}\cdot x +\textcolor{red}{x}\cdot (-2)+\textcolor{blue}{(+7)}\cdot x +\textcolor{blue}{(+7)}\cdot (-2)=x^2+\textcolor{purple}{\boxed{?}}x-14 \\$Proceed to 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 combine like terms in the expression obtained on the left side:

$\textcolor{red}{x}\cdot x +\textcolor{red}{x}\cdot (-2)+\textcolor{blue}{(+7)}\cdot x +\textcolor{blue}{(+7)}\cdot (-2)=x^2+\textcolor{purple}{\boxed{?}}x-14 \\ \downarrow\\ x^2-2x+7x-14=x^2+\textcolor{purple}{\boxed{?}}x-14 \\ x^2+5x-14=x^2+\textcolor{purple}{\boxed{?}}x-14$

Therefore the missing expression is the number 5,

Meaning - the correct answer is A.