If a = 0.346, b = 4.234and c = –4.58, then the value of a3 + b3 + c3 – 3abc is

We need to calculate the value of the expression \( a^3 + b^3 + c^3 - 3abc \) given \( a = 0.346 \), \( b = 4.234 \), and \( c = -4.58 \).

### Step 1: Calculate \( a^3 \)
\[
a^3 = (0.346)^3 = 0.041478136
\]

### Step 2: Calculate \( b^3 \)
\[
b^3 = (4.234)^3 = 75.842145304
\]

### Step 3: Calculate \( c^3 \)
\[
c^3 = (-4.58)^3 = -96.067352
\]

### Step 4: Calculate \( 3abc \)
\[
3abc = 3 \times 0.346 \times 4.234 \times (-4.58)
\]
\[
3abc = 3 \times (0.346 \times 4.234 \times -4.58) = 3 \times (-6.72135768) = -20.16407304
\]

### Step 5: Plug the values into the expression \( a^3 + b^3 + c^3 - 3abc \)
\[
a^3 + b^3 + c^3 - 3abc = 0.041478136 + 75.842145304 - 96.067352 - (-20.16407304)
\]
\[
= 0.041478136 + 75.842145304 - 96.067352 + 20.16407304
\]
\[
= 96.04769648 - 96.067352
\]
\[
= -0.01965552
\]

**Answer:** The value of \( a^3 + b^3 + c^3 - 3abc \) is approximately **-0.0197**.

Would you like to explore any more details or have any questions? Here are some related problems you might find interesting:

1. What happens if \( a = -0.346 \), \( b = -4.234 \), and \( c = 4.58 \)?
2. How does the value change if \( b \) and \( c \) are interchanged?
3. If \( a = b = c = x \), what would the expression simplify to?
4. What if \( a \), \( b \), and \( c \) are all positive integers?
5. Can you find the value of \( a^3 + b^3 + c^3 \) without computing \( 3abc \)?

**Tip:** Whenever you have a complicated expression, try simplifying it by computing each part separately.

Learn how to calculate the value of a^3 + b^3 + c^3 - 3abc with given values of a = 0.346, b = 4.234, and c = -4.58. This problem involves algebraic manipulation and the application of the cubic formula. Suitable for advanced high school students.

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