Evaluate : `15^(3)+10^(3)-25^(3)`

Options

A. `-11350`
B. `-11550`
C. `-11250`
D. `-11200`

Explanation

To evaluate \( 15^3 + 10^3 - 25^3 \), we can use the identity for the sum of cubes. The identity states that:

\[ A^3 + B^3 + C^3 - 3ABC = (A + B + C)(A^2 + B^2 + C^2 - AB - AC - BC) \]

In our case, we can let:
- \( A = 15 \)
- \( B = 10 \)
- \( C = -25 \)

Now, we can calculate \( A + B + C \):

\[ A + B + C = 15 + 10 - 25 = 0 \]

Since \( A + B + C = 0 \), we can simplify our expression using the identity:

\[ A^3 + B^3 + C^3 - 3ABC = 0 \]

This implies:

\[ A^3 + B^3 + C^3 = 3ABC \]

Next, we calculate \( 3ABC \):

\[ ABC = 15 \cdot 10 \cdot (-25) \]

Calculating \( 15 \cdot 10 \):

\[ 15 \cdot 10 = 150 \]

Now, multiplying by \(-25\):

\[ 150 \cdot (-25) = -3750 \]

Now, we can find \( 3ABC \):

\[ 3ABC = 3 \cdot (-3750) = -11250 \]

Thus, we have:

\[ A^3 + B^3 + C^3 = -11250 \]

Therefore, the final answer is:

\[ 15^3 + 10^3 - 25^3 = -11250 \]