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The expression you provided is:

\[ 8b^3 c^4 + 5b^4 c^3 - 3b^4 c^3 \]

We can begin by simplifying the expression by combining like terms:

1. The first term \(8b^3 c^4\) is already in its simplest form as there are no other terms with \(b^3 c^4\).
2. The second and third terms, \(5b^4 c^3\) and \(-3b^4 c^3\), are like terms because they share the same variables raised to the same powers.

We perform the operation:

\[ 5b^4 c^3 - 3b^4 c^3 = 2b^4 c^3 \]

Thus, the simplified expression is:

\[ 8b^3 c^4 + 2b^4 c^3 \]

This is the simplest form of the expression as the terms do not share the same exact variables with the same powers, so they cannot be combined further.

Would you like more details on this or have any questions about the simplification process?

1. What would happen if all terms had the same powers for \(b\) and \(c\)?
2. How can you factor out common terms from expressions like these?
3. What are the general rules for combining like terms?
4. How would adding another term with different variables affect the simplification?
5. What tools or techniques are useful for checking simplifications like these?

**Tip:** Always ensure that the terms you are combining have exactly the same variables raised to the same powers, as only like terms can be combined directly.

Simplify the expression: 8b^3 c^4 + 5b^4 c^3 - 3b^4 c^3

Learn how to simplify the expression 8b^3 c^4 + 5b^4 c^3 - 3b^4 c^3 by combining like terms. This step-by-step guide covers key algebraic concepts, including working with exponents and identifying like terms. Suitable for students in Grades 7-9.

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