Multiply :
`2m^(2) - 3m - 1` and `4m^(2) - m - 1`

Answer

To solve the problem of multiplying the algebraic expressions \(2m^2 - 3m - 1\) and \(4m^2 - m - 1\), we will follow a systematic approach.

### Step-by-Step Solution:

1. **Write the expressions**:
We have two expressions:
\[ A = 2m^2 - 3m - 1 \]
\[ B = 4m^2 - m - 1 \]

2. **Use the distributive property (FOIL method)**:
We will multiply each term in the first expression \(A\) by each term in the second expression \(B\).

3. **Multiply the first term of \(A\) with all terms of \(B\)**:
- \(2m^2 \cdot 4m^2 = 8m^4\)
- \(2m^2 \cdot (-m) = -2m^3\)
- \(2m^2 \cdot (-1) = -2m^2\)

4. **Multiply the second term of \(A\) with all terms of \(B\)**:
- \(-3m \cdot 4m^2 = -12m^3\)
- \(-3m \cdot (-m) = 3m^2\)
- \(-3m \cdot (-1) = 3m\)

5. **Multiply the third term of \(A\) with all terms of \(B\)**:
- \(-1 \cdot 4m^2 = -4m^2\)
- \(-1 \cdot (-m) = m\)
- \(-1 \cdot (-1) = 1\)

6. **Combine all the products**:
Now we will combine all the results from the multiplications:
\[ 8m^4 + (-2m^3 - 12m^3) + (-2m^2 + 3m^2 - 4m^2) + (3m + m) + 1 \]

7. **Combine like terms**:
- For \(m^4\): \(8m^4\)
- For \(m^3\): \(-2m^3 - 12m^3 = -14m^3\)
- For \(m^2\): \(-2m^2 + 3m^2 - 4m^2 = -3m^2\)
- For \(m\): \(3m + m = 4m\)
- Constant term: \(1\)

8. **Final expression**:
Combining all the like terms, we get:
\[ 8m^4 - 14m^3 - 3m^2 + 4m + 1 \]

### Final Answer:
\[ 8m^4 - 14m^3 - 3m^2 + 4m + 1 \]