The sun of `8x^(2)y^(2)z^(3), 12x^(2)z^(3)y^(2) " and " 15x^(2)y^(2)z^(3)` is

Options

A. `24x^(3)y^(2)z^(3)`
B. `360x^(3)y^(4)z^(3)`
C. `180x^(3)y^(3)z^(3)`
D. `35x^(2)y^(2)z^(3)`

Answer

To find the sum of the algebraic expressions \(8x^2y^2z^3\), \(12x^2z^3y^2\), and \(15x^2y^2z^3\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Terms**:
The given terms are:
- \(8x^2y^2z^3\)
- \(12x^2z^3y^2\) (which can be rearranged to \(12x^2y^2z^3\) since multiplication is commutative)
- \(15x^2y^2z^3\)

2. **Combine Like Terms**:
Since all three terms are like terms (they have the same variables with the same exponents), we can combine them by adding their coefficients:
\[ 8 + 12 + 15 \]

3. **Calculate the Sum of Coefficients**:
- First, add \(8\) and \(12\):
\[ 8 + 12 = 20 \]
- Next, add \(20\) and \(15\):
\[ 20 + 15 = 35 \]

4. **Write the Final Expression**:
Now, we can write the final expression by combining the sum of the coefficients with the common variable part:
\[ 35x^2y^2z^3 \]

### Final Answer:
The sum of the expressions is \(35x^2y^2z^3\).