Which of the following are the factors of $a^{4} - b^{4}$ ?

z-2

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z(z-2)

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2z(z-2)

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None of these

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Solution

The correct options are
A
z-2

B
z(z-2)

C
2z(z-2)

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

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