Simplify \((1 + 2\sqrt{3})^{2} - (1 - 2\sqrt{3})^{2}\)

The roots of a quadratic equation are \((3 - \sqrt{3})\) and \((3 + \sqrt{3})\). Find its equation.

If (x - 3) is a factor of \(2x^{2} - 2x + p\), find the value of constant p.

The coefficient of the 7th term in the binomial expansion of \((2 - \frac{x}{3})^{10}\) in ascending powers of x is

If \(\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = m\sqrt{2}\), where m is a constant. Find m.

Simplify \(\frac{\log_{5} 8}{\log_{5} \sqrt{8}}\).

Find the domain of \(f(x) = \frac{x}{3 - x}, x \in R\), the set of real numbers.

If \(16^{3x} = \frac{1}{4}(32^{x - 1})\), find the value of x.

Find the value of \(\cos(60° + 45°)\) leaving your answer in surd form.