Prove that:
$(a^{2} + b^{2}) (a^{2} + b^{2}) - (a^{2} - b^{2}) (a^{2} - b^{2}) = 4 a^{2} b^{2}$

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Solution

$(a^{2} + b^{2}) (a^{2} + b^{2}) - (a^{2} - b^{2}) (a^{2} - b^{2})$
$= {(a^{2} + b^{2})}^{2} - {(a^{2} - b^{2})}^{2}$
$= (a^{2} + b^{2} + a^{2} - b^{2}) (a^{2} + b^{2} - a^{2} + b^{2})$
$= (2 a^{2}) (2 b^{2})$
$= 4 a^{2} b^{2}$
Hence proved

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