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Q.

The simplified form of $x^{2} y^{2} z^{2} \times (xy - yz + zx)$ = ____.

see full answer

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Detailed Solution

The simplified form of

x^{2} y^{2} z^{2} \times (xy - yz + zx)

=

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

.
Given,

x^{2} y^{2} z^{2} \times (xy - yz + zx)

.
We know that,

(a) \times (b + c + d) = (a \times b + a \times c + a \times d)

.

x^{2} y^{2} z^{2} \times (xy - yz + zx)

=

x^{2} {xy}^{2} {yz}^{2} - x^{2} y^{2} {yz}^{2} z + x^{2} {xy}^{2} z^{2} z

=

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

So,

x^{2} y^{2} z^{2} \times (xy - yz + zx)

=

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

.
Hence, the correct answer is

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

.

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The simplified form of x2y2z2×(xy-yz + zx) = ____.