Let's perform the indicated operations and simplify the expressions step-by-step.

a. $7y^2(-y^2)$

To simplify this expression, apply the multiplication:

$7y^2 \cdot (-y^2) = 7 \cdot (-1) \cdot y^2 \cdot y^2 = -7y^{2+2} = -7y^4$

So, the simplified answer for (a) is:

$\boxed{-7y^4}$

b. $7y^2 - y^2$

This expression is a simple subtraction of like terms:

$7y^2 - y^2 = (7 - 1)y^2 = 6y^2$

So, the simplified answer for (b) is:

$\boxed{6y^2}$

c. Explanation of the Difference Between the Two Expressions

1. Expression (a): $7y^2(-y^2)$ is a multiplication operation. Here, you are multiplying $7y^2$ by $-y^2$, resulting in a higher degree polynomial ($y^4$).
2. Expression (b): $7y^2 - y^2$ is a subtraction operation between two like terms ($y^2$). The result remains a polynomial of degree 2.

Thus, the key difference is that expression (a) involves multiplication, which increases the power of $y$, while expression (b) involves subtraction of like terms, maintaining the same power.

Would you like further details, or do you have any questions?

Related Questions:

1. What is the degree of a polynomial, and how is it determined?
2. How do you perform polynomial multiplication?
3. What are like terms, and how do you combine them?
4. How does the distributive property apply to these types of problems?
5. Can you explain how to factor a polynomial?

Tip:

When simplifying algebraic expressions, always pay attention to the operations (like multiplication and subtraction) and the powers of the variables involved.