Question

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Answer 1

Explicación paso a paso:

I.

Q =

$= \frac{ {a}^{12} - {b}^{18}}{ {a}^{2} - {b}^{3}} \\ \\ = \frac{{ ({a}^{2}}) ^{6}- {({b}^{3}})^{6}}{ {a}^{2} - {b}^{3}} \\ \\ = { ({a}^{2}) }^{5} + {( {a}^{2}) }^{4} {b}^{3} + { ({a}^{2} )}^{3} { ({b}^{3}) }^{2} + {({a}^{2}} )^{2} {( {b}^{3}) }^{3} + {a}^{2} {( {b}^{3}) }^{4} + {( {b}^{3} )}^{5} \\ \\ = {a}^{10} + {a}^{8} {b}^{3} + {a}^{6} {b}^{6} + {a}^{4} {b}^{9} + {a}^{2} {b}^{12} + {b}^{15}$

II.

R =

$\frac{ {x}^{30} - {z}^{12}}{ {x}^{10} - {z}^{4}} \\ \\ = \frac{{ ({x}^{10}}) ^{3}- {({z}^{4}})^{3}}{ {x}^{10} - {z}^{4}} \\ \\ = { ({x}^{10}) }^{2} + ( {x}^{10}) {z}^{4} + { ({z}^{4} )}^{2} \\ \\ = {x}^{20} + {x}^{10} {z}^{4} + {z}^{8}$