7. $$ 17 m^{6} n^{11}-\left(5 m^{5} n^{2}\right)\left(4 m h^{9}\right) $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$ 17m^{6}n^{11} - \left(5m^{5}n^{2}\right)\left(4mh^{9}\right) $$

**Step 1: Expand the Product**

First, expand the product inside the parentheses:

$$
\left(5m^{5}n^{2}\right)\left(4mh^{9}\right) = 5 \times 4 \times m^{5} \times m \times n^{2} \times h^{9} = 20m^{6}n^{2}h^{9}
$$

**Step 2: Substitute Back into the Original Expression**

Now, substitute the expanded product back into the original expression:

$$
17m^{6}n^{11} - 20m^{6}n^{2}h^{9}
$$

**Step 3: Factor Common Terms**

Notice that both terms have common factors of $$ m^{6} $$ and $$ n^{2} $$. Factor these out:

$$
m^{6}n^{2}\left(17n^{9} - 20h^{9}\right)
$$

**Final Simplified Expression:**

$$
m^{6}n^{2}\left(17n^{9} - 20h^{9}\right)
$$
The simplified expression is $$ m^{6}n^{2}(17n^{9} - 20h^{9}) $$.

7. \( 17 m^{6} n^{11}-\left(5 m^{5} n^{2}\right)\left(4 m h^{9}\right) \)