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Let's solve the problems step-by-step:

### Problem A
We are given:
\[
A = 310^2 - 309^2
\]

This expression can be simplified using the difference of squares formula:

\[
a^2 - b^2 = (a - b)(a + b)
\]

Here, \(a = 310\) and \(b = 309\). So,

\[
A = (310 - 309)(310 + 309) = 1 \times 619 = 619
\]

Thus, \(A = 619\).

### Problem B
We are given:
\[
B = 25310^2 - 25309 \times 25311
\]

Notice that:

\[
25310^2 = 25310 \times 25310
\]
and the expression \(25309 \times 25311\) is also a difference of squares:
\[
(a - 1)(a + 1) = a^2 - 1, \quad \text{where } a = 25310.
\]

So,
\[
25309 \times 25311 = 25310^2 - 1.
\]

Substituting this in, we get:

\[
B = 25310^2 - (25310^2 - 1) = 1.
\]

Thus, \(B = 1\).

### Final Answers
- \(A = 619\)
- \(B = 1\)

Would you like more details or have any questions? 

Here are five related questions to explore further:
1. What is the difference of squares formula, and why is it useful in algebra?
2. How do you simplify expressions involving powers and products?
3. Can you solve another example of a difference of squares?
4. How do you factor more complex polynomials?
5. How do different algebraic formulas relate to each other?

**Tip:** Remember that recognizing patterns like the difference of squares can save a lot of time in algebraic calculations!

Calculate A = 310^2 - 309^2 and B = 25310^2 - 25309 * 25311.

Learn how to solve problems involving the difference of squares formula with examples like A = 310^2 - 309^2 and B = 25310^2 - 25309 * 25311. Understand the key steps and algebraic concepts for simplifying these expressions. Suitable for students in Grades 9-12.

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