To simplify the expression \((4x + 2)(5x - 7)\), we need to use the distributive property (also known as the FOIL method for binomials). This method involves multiplying each term in the first binomial by each term in the second binomial:

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

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: \(2 \cdot (-7) = -14\)

Now, combine all these products:

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

Next, combine the like terms:

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

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

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

Do you want more details or have any questions?

Here are 8 related questions that might expand your understanding:

1. How do you multiply binomials using the distributive property?
2. What is the FOIL method, and how does it apply to binomials?
3. How do you identify and combine like terms in a polynomial?
4. Can you expand the expression \((x + 3)(2x - 4)\)?
5. How does the distributive property work for expressions with more than two terms?
6. What are the key differences between binomials, trinomials, and polynomials?
7. How can you verify the result of multiplying binomials?
8. What are some common mistakes to avoid when expanding binomials?

**Tip:** Always double-check your multiplication and ensure you combine like terms correctly to avoid errors in polynomial expansion.

Learn how to simplify the expression (4x + 2)(5x - 7) step-by-step using the distributive property. This problem involves algebraic concepts such as binomial expansion and polynomials. Suitable for students in Grades 7-9.

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