A designer is calculating the area of a square graphic with a side length of $(1 + 3\sqrt{6})$ units. Using the identity $(a + b)^2 = a^2 + 2ab + b^2$, match each part of the expanded pattern to its correct simplified value in this calculation.

An interior designer is calculating the square footage of a decorative wall panel that has a side length of $(10 + \sqrt{2})$ feet. Using the binomial squares pattern $(a + b)^2 = a^2 + 2ab + b^2$ to calculate the area $(10 + \sqrt{2})^2$, which of the following is the final simplified expression?

A landscape architect is designing a square stone patio with a side length of $(1 + 3\sqrt{6})$ feet. To calculate the area of the patio, the architect squares the side length using the binomial squares pattern $(a + b)^2 = a^2 + 2ab + b^2$. After substituting the values $a = 1$ and $b = 3\sqrt{6}$ into the pattern, the value of the third term, $b^2$ (which is $(3\sqrt{6})^2$), simplifies to the integer ____.

A carpenter is calculating the total area of a square wooden deck with a side length of $({}1 + 3\sqrt{6})$ feet. To find the total area, the carpenter must expand the expression $({}1 + 3\sqrt{6})^2$ using the binomial squares pattern $(a + b)^2 = a^2 + 2ab + b^2$. Arrange the following steps in the correct order to simplify this calculation.

A site surveyor calculates the area of a square plot with a side length of $(10 + \sqrt{2})$ meters. They expand the expression $(10 + \sqrt{2})^2$ and report that the simplified exact area is 102 square meters. This calculation is correct.