Question

What is `(-9w^4 + 7w^2) -: -w`?

Answer 1

`-9w^3+7w`

Explanation:

Given:`" "(-9w^4+7w^2)-:w`

After a while you will get more used to this type of question and be able to jump steps, doing it much faster.
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Write as:`" "(-9w^4+7w^2)/w`

This is the same as:`" "(-9w^4)/w+(7w^2)/w`
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`color(blue)("Consider the "(-9w^4)/w`

This is`" "(-9xxwxxwxxwxxw)/w`

Using one `w` from the top (numerator)and the `w` from the bottom (denominator) we have:

`" "-9xxwxxwxxwxx w/w`

But `w/w=1" and "wxxwxxw = w^3" giving:"`

`color(blue)(-9w^3)`

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`color(blue)("Consider the "(+7w^2)/w`

Using the same method as above we end up with:

`" "color(blue)(+7w)`
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`color(blue)("Putting at all together")`

`color(green)((-9w^4+7w^2)-:w = -9w^3+7w)`