Subtract:
$p^{2} - 2 p q + q^{2}$ from $p^{2} + 2 p q - q^{2}$

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Solution

Trying to factor a multi variable polynomial :

Factoring p² - 2pq + q²
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (p - q)•(p - q)

Detecting a perfect square : p² -2pq +q² is a perfect square
It factors into (p-q)•(p-q)
which is another way of writing (p-q)²
How to recognize a perfect square trinomial:
• It has three terms
• Two of its terms are perfect squares themselves

• The remaining term is twice the product of the square roots of the other two terms

Final result :

(p - q)²

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(p^{2} - 2 p q + q^{2}) - r^{2}

tan θ = \frac{p^{2} - q^{2}}{2 p q}

- r^{2} + p^{2} + q^{2} - 2 p q

(p + q)² = p² + 2pq + q² = 1 represents an equation used in:

(p^{2} - q^{2}) = 2 (p q - q^{2})

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