As a manufacturing technician calculating material dimensions, you need to determine the exact area of a square component with a side length of $(6 - \sqrt{5})$ centimeters. To find the area, you must expand the expression $(6 - \sqrt{5})^2$. Recalling the Binomial Squares Pattern, what is the exact expanded form of this expression before combining the numerical terms?

A precision machinist is calculating the area of a square metal plate with a side length of $9 - 2\sqrt{10}$millimeters. To determine the area, the machinist must expand and simplify the expression$(9 - 2\sqrt{10})^2$. Arrange the following steps in the correct order to simplify this expression using the Binomial Squares Pattern.

A solar panel installer is calculating the surface area of a square mounting bracket with a side length of $({}9 - 2\sqrt{10})$ inches. To find the area, the installer must expand the expression $({}9 - 2\sqrt{10})^2$ using the Binomial Squares Pattern: $(a - b)^2 = a^2 - 2ab + b^2$. Match each component of the pattern with the correct simplified value it produces in this calculation.

Quality Control in Area Calculations

A precision machinist is calculating the area of a square component with a side length of `${}9 - 2\sqrt{10}$ millimeters. To find the area, the machinist expands the expression $({}9 - 2\sqrt{10})^2$ using the binomial squares pattern $(a - b)^2 = a^2 - 2ab + b^2$. After calculating and combining the numerical constant terms $a^2$ and $b^2$, the resulting constant value in the simplified expression is ____.