https://file.aiquickdraw.com/mathbot/file/1726457534432z3t3a1g1.jpg

The expression shown in the image is:

\[
5b^3d^2 + \left(6bd - 7b^3d^2\right)
\]

To simplify this, we can proceed step-by-step:

1. First, distribute the parentheses:
   \[
   5b^3d^2 + 6bd - 7b^3d^2
   \]

2. Now, combine like terms. Notice that \(5b^3d^2\) and \(-7b^3d^2\) are like terms:
   \[
   (5b^3d^2 - 7b^3d^2) + 6bd = -2b^3d^2 + 6bd
   \]

So, the simplified expression is:

\[
-2b^3d^2 + 6bd
\]

Would you like more details or explanations on this process? 

Here are some related questions to deepen understanding:

1. What are like terms, and why can we combine them in this expression?
2. How does the degree of a term affect simplification?
3. How would this expression change if \(d = 1\)?
4. Can you factor the final expression for specific values of \(b\) or \(d\)?
5. What is the role of distribution in simplifying algebraic expressions?

**Tip:** Always look for like terms to combine when simplifying expressions; this makes the expression more manageable.

Simplify the algebraic expression: 5b^3d^2 + (6bd - 7b^3d^2).

Learn how to simplify the algebraic expression 5b^3d^2 + (6bd - 7b^3d^2) by combining like terms. This step-by-step explanation covers the distributive property and the process of identifying and combining terms with similar variables and powers. Suitable for students in Grades 7-10.

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