Let and . Evaluate…

MATHEMATICS · Single correct · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

Let

p = \sqrt{5} + \sqrt{3}

and

q = \sqrt{5} - \sqrt{3}

. Evaluate

(p^{2} - q^{2})\,(\sqrt{5} + \sqrt{3})

. (a)

8\sqrt{5} + 12\sqrt{2}

(b)

10\sqrt{3} + 6\sqrt{5}

(c)

20\sqrt{3} + 12\sqrt{5}

(d)

2\sqrt{15} + 6