What is p^4q^2 + p^2q^4 equal to ?

Explanation

Factoring the expression gives p^2q^2(p^2 + q^2). Using the values derived for p and q: p^2q^2 = \sin^{2/3}\theta \cos^{2/3}\theta. Also, p^2+q^2 = \frac{\cos^4\theta + \sin^4\theta}{\text{something}}... No, p^2 = \frac{\cos^{4/3}\theta}{\sin^{2/3}\theta} and q^2 = \frac{\sin^{4/3}\theta}{\cos^{2/3}\theta}. Their sum is \frac{\cos^2\theta + \sin^2\theta}{\sin^{2/3}\theta \cos^{2/3}\theta} = \frac{1}{\sin^{2/3}\theta \cos^{2/3}\theta}. Multiplying this by p^2q^2 exactly cancels out the denominator, leaving 1.

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