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−4pb+2p×3b combine and simplify please

To simplify the expression \(6bp^2 - 4pb + 2p \times 3bp\), we need to follow these steps:

1. **Identify like terms**: Terms that have the same variables raised to the same powers.

2. **Perform the multiplication**: Multiply \(2p \times 3bp\).

3. **Combine like terms**: Add or subtract the coefficients of the like terms.

Let's go through these steps:

### Step 1: Identify Like Terms
In the expression \(6bp^2 - 4pb + 2p \times 3bp\):

- \(6bp^2\) is a term with variables \(b\) and \(p^2\).
- \(-4pb\) is a term with variables \(p\) and \(b\).
- \(2p \times 3bp\) needs to be simplified.

### Step 2: Perform the Multiplication
Multiply \(2p \times 3bp\):

\[
2p \times 3bp = 6bp^2
\]

### Step 3: Combine Like Terms
Now, substitute the result back into the expression:

\[
6bp^2 - 4pb + 6bp^2
\]

Combine the like terms \(6bp^2\) and \(6bp^2\):

\[
(6bp^2 + 6bp^2) - 4pb = 12bp^2 - 4pb
\]

### Simplified Expression
The simplified expression is:

\[
12bp^2 - 4pb
\]

This is the simplest form as there are no more like terms to combine.

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If you have any questions or need further explanation, feel free to ask!

Here are some related questions to explore further:

1. How do you identify like terms in algebraic expressions?
2. What is the distributive property and how is it used in simplification?
3. How can you simplify expressions involving multiple variables?
4. What are some common mistakes to avoid when simplifying algebraic expressions?
5. How do you factor out common terms in algebraic expressions?
6. What is the role of coefficients in simplifying expressions?
7. How do you apply exponent rules in simplifying expressions?
8. What are some strategies for checking your work in algebra?

**Tip:** Always double-check your work for errors by substituting numbers for the variables to verify that both the original and simplified expressions yield the same results.

Learn how to combine and simplify the algebraic expression 6bp^2 - 4pb + 2p × 3bp step-by-step. This problem covers key algebraic concepts such as combining like terms and multiplication of algebraic expressions. Suitable for high school students.

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