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The problem provided is to multiply and fill in the blanks for the expression:

\[
(7 - 3x)(2x - 5)
\]

We can solve this by using the distributive property (also known as the FOIL method for binomials), where we multiply each term in the first binomial by each term in the second binomial:

1. First: \(7 \times 2x = 14x\)
2. Outer: \(7 \times -5 = -35\)
3. Inner: \(-3x \times 2x = -6x^2\)
4. Last: \(-3x \times -5 = 15x\)

Now, combine like terms:

\[
-6x^2 + (14x + 15x) - 35 = -6x^2 + 29x - 35
\]

Thus, the completed expression is:

\[
-6x^2 + 29x - 35
\]

The correct numbers to fill in the blanks are:
- First blank: **-6**
- Second blank: **29**
- Third blank: **35**

Would you like further details or have any other questions?

Here are 5 related questions to expand your understanding:
1. How does the distributive property work in other polynomial expressions?
2. What happens when you multiply polynomials of more than two terms?
3. Can you explain the FOIL method more generally?
4. How can you apply the distributive property to factor polynomials?
5. What would change if the signs in the binomials were different?

**Tip:** When multiplying binomials, always ensure that like terms are properly combined for simplicity and accuracy.

Learn how to expand and simplify the binomial expression (7 - 3x)(2x - 5) using the distributive property and FOIL method. This problem covers key algebraic concepts in quadratic expressions, suitable for students in Grades 8-10.

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