Let's solve the problem step by step.

Step 1: Write down the given polynomials

1. First polynomial: $7y^2 + 6xy$
2. Second polynomial: $-2xy + 3$

Step 2: Subtract the second polynomial from the first

$(7y^2 + 6xy) - (-2xy + 3)$

Step 3: Distribute the negative sign across the second polynomial

$7y^2 + 6xy + 2xy - 3$

Step 4: Combine like terms

• Combine the $xy$ terms: $6xy + 2xy = 8xy$
• The $y^2$ term stays as $7y^2$.
• The constant $-3$ remains as is.

So, the simplified expression is: $7y^2 + 8xy - 3$

Conclusion

The correct answer is:

• $7y^2 + 8xy - 3$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you subtract polynomials when they have different numbers of terms?
2. What is the importance of distributing the negative sign when subtracting polynomials?
3. Can you explain how to identify and combine like terms?
4. How do operations on polynomials relate to solving algebraic equations?
5. What is the difference between adding and subtracting polynomials?

Tip: Always double-check the sign changes when subtracting polynomials to avoid errors.