(e) Expand and simplify \[ (7+\sqrt{3})(4-\sqrt{3}) \] (i)

Step 1 ：Given the expression \((7+\sqrt{3})(4-\sqrt{3})\).

Step 2 ：We can use the distributive property (also known as the FOIL method) to multiply each term in the first binomial by each term in the second binomial. The FOIL method stands for First, Outer, Inner, and Last, which refers to the terms that are multiplied together.

Step 3 ：First, we multiply the first terms in each binomial: \(7 * 4 = 28\).

Step 4 ：Next, we multiply the outer terms: \(7 * -\sqrt{3} = -7\sqrt{3}\).

Step 5 ：Then, we multiply the inner terms: \(\sqrt{3} * 4 = 4\sqrt{3}\).

Step 6 ：Finally, we multiply the last terms: \(\sqrt{3} * -\sqrt{3} = -3\).

Step 7 ：Adding these together, we get \(28 - 7\sqrt{3} + 4\sqrt{3} - 3 = 25 - 3\sqrt{3}\).

Step 8 ：\(\boxed{25 - 3\sqrt{3}}\) is the simplified form of the expression \((7 + \sqrt{3})(4 - \sqrt{3})\).