https://r2.erweima.ai/mathbot/image/1726977792304fakxj80x.jpg

The expression in the image is:

\[
100a^2b^3c - 150ab^2c^2
\]

### Step-by-step simplification:

1. **Factor out common terms**: 
   Both terms contain \( a \), \( b^2 \), and \( c \), so let's factor those out:
   \[
   a \cdot b^2 \cdot c \cdot \left( 100a \cdot b - 150c \right)
   \]

2. **Simplify the expression inside the parentheses**:
   The expression inside the parentheses is:
   \[
   100ab - 150c
   \]

   Factor out the greatest common factor of 50:
   \[
   50(2ab - 3c)
   \]

3. **Final factored form**:
   The expression can now be written as:
   \[
   50abc \cdot b \cdot (2ab - 3c)
   \]

Thus, the fully factored form is:
\[
50ab^2c(2ab - 3c)
\]

Would you like any further explanation or help with this expression?

Here are 5 related questions that could help you practice this further:

1. Would you like to explore more examples of factoring complex polynomials?
2. Should we evaluate this expression for specific values of \( a \), \( b \), and \( c \)?
3. Do you want to expand the factored form back to verify the correctness?
4. Would you like to simplify similar expressions with different powers of variables?
5. Are you interested in applying this to solve equations or word problems?

**Tip:** Always look for common factors first when factoring. It simplifies the process and makes solving complex expressions easier.

Simplify the expression: 100a^2b^3c - 150ab^2c^2

Explore the step-by-step simplification of the polynomial 100a^2b^3c - 150ab^2c^2. This guide includes factoring out the greatest common factor and further simplification, suitable for high school students learning advanced algebra.

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