(ii) $$ 7 c d\left(d^{2}-2\right)-3 c d^{2}\left(8 d+5 c^{3}\right) $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
7cd\left(d^{2} - 2\right) - 3cd^{2}\left(8d + 5c^{3}\right)
$$

**Step 1: Expand Each Term**

1. **Expand the first term:**
   $$
   7cd(d^2 - 2) = 7c d^3 - 14c d
   $$

2. **Expand the second term:**
   $$
   -3cd^{2}(8d + 5c^{3}) = -24c d^3 - 15c^4 d^2
   $$

**Step 2: Combine Like Terms**

Now, combine the expanded terms:
$$
7c d^3 - 14c d - 24c d^3 - 15c^4 d^2
$$

Combine the $$ c d^3 $$ terms:
$$
7c d^3 - 24c d^3 = -17c d^3
$$

So, the expression simplifies to:
$$
-17c d^3 - 15c^4 d^2 - 14c d
$$

**Final Simplified Form:**
$$
-15c^4 d^2 - 17c d^3 - 14c d
$$
The simplified form of the expression is: $$ -15c^4 d^2 - 17c d^3 - 14c d $$

(ii) \( 7 c d\left(d^{2}-2\right)-3 c d^{2}\left(8 d+5 c^{3}\right) \)