If x = 1, y = - 2 and z = 3. find the value of
(i) `x^(3) + y^(3) + z^3-3xyz` (ii) `3xy^(4) - 15 x^(2) y + 4z`

Options

A. `38 , 90`
B. `28 , 90`
C. `38 , 80`
D. `28 , 80`

Explanation

Let's solve the problem step by step.

### Given:
- \( x = 1 \)
- \( y = -2 \)
- \( z = 3 \)

### (i) Find the value of \( x^3 + y^3 + z^3 - 3xyz \)

1. **Calculate \( x^3 \)**:
\[ x^3 = 1^3 = 1 \]

2. **Calculate \( y^3 \)**:
\[ y^3 = (-2)^3 = -8 \]

3. **Calculate \( z^3 \)**:
\[ z^3 = 3^3 = 27 \]

4. **Calculate \( 3xyz \)**:
\[ 3xyz = 3 \times 1 \times (-2) \times 3 = 3 \times (-6) = -18 \]

5. **Combine all the values**:
\[ x^3 + y^3 + z^3 - 3xyz = 1 + (-8) + 27 - (-18) \]
\[ = 1 - 8 + 27 + 18 \]
\[ = -7 + 27 + 18 \]
\[ = 20 + 18 = 38 \]

### (ii) Find the value of \( 3xy^4 - 15x^2y + 4z \)

1. **Calculate \( y^4 \)**:
\[ y^4 = (-2)^4 = 16 \]

2. **Calculate \( 3xy^4 \)**:
\[ 3xy^4 = 3 \times 1 \times 16 = 48 \]

3. **Calculate \( x^2 \)**:
\[ x^2 = 1^2 = 1 \]

4. **Calculate \( -15x^2y \)**:
\[ -15x^2y = -15 \times 1 \times (-2) = 30 \]

5. **Calculate \( 4z \)**:
\[ 4z = 4 \times 3 = 12 \]

6. **Combine all the values**:
\[ 3xy^4 - 15x^2y + 4z = 48 + 30 + 12 \]
\[ = 90 \]

### Final Answers:
- (i) \( x^3 + y^3 + z^3 - 3xyz = 38 \)
- (ii) \( 3xy^4 - 15x^2y + 4z = 90 \)

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