As a quality control analyst in manufacturing, you are verifying a dimensional tolerance calculation originally documented as the product of conjugates: $(3-2\sqrt{5})(3+2\sqrt{5})$. Recalling the Product of Conjugates pattern, what is the fully simplified integer value of this expression?

A technician is following a technical manual to determine a calibration constant for a power generator. The manual requires simplifying the expression $(3-2\sqrt{5})(3+2\sqrt{5})$ using the Product of Conjugates pattern: $(a-b)(a+b) = a^2 - b^2$. Arrange the following steps in the correct order to find the final simplified value.

A quality control technician is using a calibration formula that simplifies to the expression $(3-2\sqrt{5})(3+2\sqrt{5})$. Using the Product of Conjugates pattern, what is the final simplified integer value the technician should record? ____

An architectural technician is verifying a structural stress calculation that simplifies to the conjugate product $(3 - 2\sqrt{5})(3 + 2\sqrt{5})$. Using the Product of Conjugates pattern $(a - b)(a + b) = a^2 - b^2$, match each part of the pattern to its specific numerical value in this calculation.

A laboratory technician is simplifying the expression $(3-2\sqrt{5})(3+2\sqrt{5})$ to determine a microscope's calibration factor. Using the Product of Conjugates pattern $(a-b)(a+b) = a^2 - b^2$, the technician identifies that the square of the second term, $(2\sqrt{5})^2$, is equal to 20. Is the technician's identification correct?

Product of Conjugates Pattern Identification

Verifying Structural Stress Formulas in Construction Planning