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

y^{- 1} z^{3} + x y^{2}

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x y^{- 1} z^{3} + x y^{2} z

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y^{- 1} z^{3} + x y^{2} z

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x y^{- 1} z^{3} + x y^{2}

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Solution

The correct option is A $y^{- 1} z^{3} + x y^{2}$
We use distributive law to multiply a monomial and a binomial, as shown below:
$(x^{- 1} y z^{2}) (x y^{- 2} z + x^{2} y z^{- 2})$
$= (x^{- 1} y z^{2} \times x y^{- 2} z)$ + $(x^{- 1} y z^{2} \times x^{2} y z^{- 2})$
$= y^{- 1} z^{3} + x y^{2}$

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