Using the identity $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ compute $(p^{2} - q^{2})^{2}$ ;

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Solution

Using Identity $(a - b)^{2}$ = $a^{2} - 2 a b + b^{2}$
We have: $(p^{2} - q^{2})^{2}$
Therefore, $(p^{2} - q^{2})^{2}$ = $(p^{2})^{2} - 2 (p^{2}) (q^{2}) + (q^{2})^{2}$ $=$ $p^{4} - 2 p^{2} q^{2} + q^{4}$
The answer is $p^{4} - 2 p^{2} q^{2} + q^{4}$

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