To simplify the expression \(4(2p - 4) + 7(3p - 2)\), you need to distribute the constants outside the parentheses to the terms inside and then combine like terms. Here's the step-by-step process:

1. Distribute the 4 in the first part:

   \[
   4(2p - 4) = 4 \cdot 2p - 4 \cdot 4 = 8p - 16
   \]

2. Distribute the 7 in the second part:

   \[
   7(3p - 2) = 7 \cdot 3p - 7 \cdot 2 = 21p - 14
   \]

3. Combine the results from both parts:

   \[
   8p - 16 + 21p - 14
   \]

4. Combine the like terms (\(8p\) and \(21p\)):

   \[
   (8p + 21p) + (-16 - 14) = 29p - 30
   \]

So, the simplified expression is:

\[
29p - 30
\]

Would you like more details or have any questions?

Here are 5 related questions you might find useful:

1. How do you distribute numbers in algebraic expressions?
2. What are the steps to simplify an expression with multiple distribution operations?
3. How can you identify and combine like terms in a complex expression?
4. What is the distributive property, and how is it used in algebra?
5. How can simplifying expressions help in solving algebraic equations?

**Tip:** When simplifying expressions, carefully distribute and combine like terms to avoid common mistakes with signs and coefficients!

Learn how to simplify the expression 4(2p - 4) + 7(3p - 2) with a detailed step-by-step solution. This problem covers key algebraic concepts, including the distributive property and combining like terms. Suitable for students in Grades 7-9.

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