You are correct, there was an error in the calculation. Let's re-evaluate the combination of the like terms step-by-step:

Starting from:

\[
(4x + 2)(5x - 7)
\]

1. Multiply the first terms: \(4x \cdot 5x = 20x^2\)
2. Multiply the outer terms: \(4x \cdot (-7) = -28x\)
3. Multiply the inner terms: \(2 \cdot 5x = 10x\)
4. Multiply the last terms: \(2 \cdot (-7) = -14\)

Combining these products, we get:

\[
20x^2 - 28x + 10x - 14
\]

Now, correctly combine the like terms (\(-28x\) and \(10x\)):

\[
-28x + 10x = -18x
\]

Thus, the corrected simplified form of \((4x + 2)(5x - 7)\) is:

\[
20x^2 - 18x - 14
\]

So, the error was a typo in my previous message. Thank you for catching that.

Do you want more details or have any questions?

Here are 8 related questions that might expand your understanding:

1. How do you ensure accuracy when combining like terms in polynomial expressions?
2. Can you expand the expression \((3x + 4)(2x - 5)\)?
3. What are the common pitfalls when using the distributive property in algebra?
4. How can you use polynomial multiplication in solving real-world problems?
5. How do you factor polynomials back into their binomial components?
6. Can you explain the process of polynomial long division?
7. What strategies can you use to check your work when expanding polynomials?
8. How does polynomial multiplication relate to functions and their graphs?

**Tip:** Always double-check each step in your calculations to ensure accuracy, especially when combining like terms in polynomials.

Explore the concept of polynomial multiplication and combining like terms in algebra. This detailed explanation includes step-by-step examples and common pitfalls to avoid. Suitable for students in Grades 7-9.

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