Question

Find the quotient: (36u6v5−24u4v3)÷(−4u3v2)

Answer 1

Explanation:

Let's go through the steps again to clarify the simplification of the expression
`\(\frac{{36u^6v^5 - 24u^4v^3}}{{-4u^3v^2}}\)`:

Start with the expression:
`\(\frac{{36u^6v^5 - 24u^4v^3}}{{-4u^3v^2}}\)`.

Factor out the common terms from the numerator:

`\[ \frac{{12u^4v^3(3u^2v^2 - 2)}}{{-4u^3v^2}} \]`

Cancel out common factors from the numerator and denominator:

`\[ \frac{{12u^4v^3}}{{-4u^2}} \]`

Simplify the coefficients:

`\[ -3u^2v^3 \]`

Now, to express this answer in a factored form, we can factor out a common factor of
`\(-3uv\)`:

`\[ -3u^2v^3 = -3uv(3u^2v^2 - 2) \]`

So, the simplified and factored form of the expression is indeed
`\(-3uv(3u^2v^2 - 2)\)`.