Question

1. $(3sqrt{6} + 2sqrt{7})(3sqrt{6} - 2sqrt{7})$

Explanation:

Step1: Identify the formula

This is a difference of squares: \((a + b)(a - b)=a^2 - b^2\). Let \(a = 3\sqrt{6}\) and \(b = 2\sqrt{7}\).

Step2: Apply the formula

Calculate \(a^2=(3\sqrt{6})^2 = 3^2\times(\sqrt{6})^2=9\times6 = 54\).
Calculate \(b^2=(2\sqrt{7})^2 = 2^2\times(\sqrt{7})^2=4\times7 = 28\).

Step3: Subtract \(b^2\) from \(a^2\)

\(a^2 - b^2=54 - 28 = 26\).

Answer:

26