Factorise the following polynomial.
$x y (z^{2} + 1) + z (x^{2} + y^{2})$

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Solution

$x y (z^{2} + 1) + z (x^{2} + y^{2})$

$= x y z^{2} + x y + z x^{2} + z y^{2}$

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

$= z x (y z + x) + y (x + y z)$

$= z x (x + y z) + y (x + y z)$

$= (x + y z) (z x + y)$

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Similar questions

x y (z^{2} + 1) + z (x^{2} + y^{2})

x y (z^{2} + 1) + z (x^{2} + y^{2})

xy(z² + 1) + z(x²+ y²) can be factorise as

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

x^{2} - y^{2} + 2 x + 1

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