Multiply $(x^{2} + 4 y^{2} + z^{2})$ by $(z + x)$ .

x^{3} z + x^{4} + 4 y^{2} z + 4 y^{2} x + z^{2} + z^{2} x

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x^{2} z + x^{3} + 4 y^{2} z + 4 y^{2} x + z^{3} + z^{2} x

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x^{3} z + x^{4} + 4 y^{2} z + 4 y^{3} x + z^{3} + z^{2} x

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x^{3} z + x^{3} + 4 y^{2} z + 4 y^{2} x + z^{3} + z^{2} x

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Solution

The correct option is B $x^{2} z + x^{3} + 4 y^{2} z + 4 y^{2} x + z^{3} + z^{2} x$
$(x^{2} + 4 y^{2} + z^{2}) (z + x)$
$= z (x^{2} + 4 y^{2} + z^{2}) +$ $x (x^{2} + 4 y^{2} + z^{2})$
$= x^{2} z + 4 y^{2} z + z^{3} + x^{3} + 4 x y^{2} + x z^{2}$
$= x^{2} z + x^{3} + 4 y^{2} z + 4 y^{2} x + z^{3} + z^{2} x$

Hence, option B is correct.

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Similar questions

Let x, y, z be positive reals. Which of the following implies x = y = z?

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