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

(x - y - z)

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(x + y + z)

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

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Solution

The correct options are
A $(x - y - z)$
B $(x + y + z)$
C $(x^{2} + y^{2} + z^{2} + 2 y z)$
D 1
$x^{4} - (y + z)^{4}$
$= (x^{2})^{2} - {(y + z)^{2}}^{2}$
$= (x^{2} + (y + z)^{2}) (x^{2} - (y + z)^{2})$
$= (x^{2} + (y + z)^{2}) (x + y + z) (x - y - z)$
$= (x^{2} + y^{2} + z^{2} + 2 y z) (x + y + z) (x - y - z)$
$= 1 \times (x^{2} + y^{2} + z^{2} + 2 y z) \times (x + y + z) \times (x - y - z)$

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