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Division of a Monomial by Another Monomial

Factors of ...

Question

Factors of $x^{4} - (x - z)^{4}$ are

(2 x^{2} - 2 x z + z^{2})

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2 x - z

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z

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x

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Solution

The correct options are
A $(2 x^{2} - 2 x z + z^{2})$
B $2 x - z$
C $z$
$x^{4} - (x - z)^{4}$
$= (x^{2})^{2} - {{(x - z)}^{2}}^{2}$
$= (x^{2} + (x - z)^{2}) (x^{2} - (x - z)^{2})^{2}$
$= (x^{2} + x^{2} - 2 x z + z^{2}) (x + x - z) (x - x + z)$
$= (2 x^{2} - 2 x z + z^{2}) (2 x - z) (z)$

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