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The given problem is:

\[
6y^2 (8y^2 - 5y + 2)
\]

To solve this, we need to distribute \(6y^2\) to each term inside the parentheses.

### Step-by-Step Expansion
1. Multiply \(6y^2\) by \(8y^2\):

   \[
   6y^2 \times 8y^2 = 48y^4
   \]

2. Multiply \(6y^2\) by \(-5y\):

   \[
   6y^2 \times (-5y) = -30y^3
   \]

3. Multiply \(6y^2\) by \(2\):

   \[
   6y^2 \times 2 = 12y^2
   \]

### Final Expression
Combining all these results, we get:

\[
48y^4 - 30y^3 + 12y^2
\]

So the answer is:

\[
6y^2 (8y^2 - 5y + 2) = 48y^4 - 30y^3 + 12y^2
\]

Would you like any more details about this process or have any further questions?

Here are some related questions you might find helpful:
1. What is the distributive property and how does it work?
2. How do you multiply two polynomials?
3. Can you explain the process of combining like terms?
4. What are the key rules for multiplying powers with the same base?
5. How do different properties of exponents apply to polynomial multiplication?

**Tip**: Always remember to distribute every term in the monomial to each term in the polynomial carefully to avoid mistakes in signs or coefficients.

Find the product of the monomial and the polynomial: 6y^2(8y^2 - 5y + 2).

Learn how to multiply the monomial 6y^2 by the polynomial 8y^2 - 5y + 2 using the distributive property. This detailed solution walks through each step, resulting in 48y^4 - 30y^3 + 12y^2, and is suitable for students in Grades 8-10.

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