https://r2.erweima.ai/mathbot/image/1726325269451nxs946p3.jpg

Let's solve the two products given in the image:

**a.** \((5m^2)(-3m^2n + 8)\)

We distribute \(5m^2\) to both terms inside the parentheses:

\[
5m^2 \cdot (-3m^2n) + 5m^2 \cdot 8
\]

This gives:

\[
-15m^4n + 40m^2
\]

So, the answer for part **a** is:

\[
-15m^4n + 40m^2
\]

---

**b.** \((9x - y - 7y)(-3xy)\)

Here we distribute \(-3xy\) to each term inside the parentheses:

\[
(-3xy) \cdot 9x + (-3xy) \cdot (-y) + (-3xy) \cdot (-7y)
\]

Calculating each term:

\[
-27x^2y + 3xy^2 + 21xy^2
\]

Now, combining like terms:

\[
-27x^2y + (3xy^2 + 21xy^2) = -27x^2y + 24xy^2
\]

So, the answer for part **b** is:

\[
-27x^2y + 24xy^2
\]

---

Would you like further details or explanations?

Here are some related questions:
1. How do you apply the distributive property in polynomial multiplication?
2. What are the common mistakes when multiplying expressions like these?
3. How do you factor a polynomial after multiplying it?
4. What role do exponents play when multiplying terms like \(m^2\) and \(x^2\)?
5. How can you simplify expressions like \(3xy^2 + 21xy^2\)?

**Tip:** When multiplying polynomials, keep track of like terms to simplify the final expression easily.

Realiza los siguientes productos: a. (5m^2)(-3m^2n + 8) b. (9x - y - 7y)(-3xy)

Learn how to solve polynomial multiplication problems like (5m^2)(-3m^2n + 8) and (9x - y - 7y)(-3xy) using the distributive property. This step-by-step solution is suitable for students in Grades 8-10.

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