What is the following product? \( (x \sqrt{7}-3 \sqrt{8})(x \sqrt{7}-3 \sqrt{8}) \)

The expression \( (x \sqrt{7} - 3 \sqrt{8})(x \sqrt{7} - 3 \sqrt{8}) \) can be simplified as a perfect square. It equals \( (x \sqrt{7} - 3 \sqrt{8})^2 \). To expand it, use the formula \( (a - b)^2 = a^2 - 2ab + b^2 \). Here, \( a = x \sqrt{7} \) and \( b = 3 \sqrt{8} \). Calculating: 1. \( a^2 = (x \sqrt{7})^2 = 7x^2 \) 2. \( b^2 = (3 \sqrt{8})^2 = 9 \cdot 8 = 72 \) 3. \( 2ab = 2(x \sqrt{7})(3 \sqrt{8}) = 6 \sqrt{56} x = 6 \cdot 2\sqrt{14} x = 12 \sqrt{14} x \) Putting it all together, you get: \[ 7x^2 - 12 \sqrt{14} x + 72 \] So the final expanded form is \( 7x^2 - 12 \sqrt{14} x + 72 \).