Compute the following
(i) `2xx6!-3xx5!`
(ii) `3xx4!+7xx4!`

Answer

Let's solve the given problems step by step.

### Problem (i): Compute `2 × 6! - 3 × 5!`

1. **Rewrite Factorials**:
- Recall that \(6! = 6 \times 5!\). Therefore, we can rewrite the expression:
\[ 2 \times 6! = 2 \times (6 \times 5!) = 12 \times 5! \]
Now the expression becomes:
\[ 12 \times 5! - 3 \times 5! \]

2. **Factor Out \(5!\)**:
- We can factor out \(5!\) from both terms:
\[ (12 - 3) \times 5! = 9 \times 5! \]

3. **Calculate \(5!\)**:
- Now, calculate \(5!\):
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]

4. **Final Calculation**:
- Substitute \(5!\) back into the expression:
\[ 9 \times 120 = 1080 \]

Thus, the result for part (i) is **1080**.

### Problem (ii): Compute `3 × 4! + 7 × 4!`

1. **Factor Out \(4!\)**:
- Similar to the previous problem, we can factor out \(4!\):
\[ 3 \times 4! + 7 \times 4! = (3 + 7) \times 4! = 10 \times 4! \]

2. **Calculate \(4!\)**:
- Now, calculate \(4!\):
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]

3. **Final Calculation**:
- Substitute \(4!\) back into the expression:
\[ 10 \times 24 = 240 \]

Thus, the result for part (ii) is **240**.

### Summary of Results:
- (i) \(2 \times 6! - 3 \times 5! = 1080\)
- (ii) \(3 \times 4! + 7 \times 4! = 240\)