Let's break down the expression step by step to simplify and solve it.

The expression given is:

\[
(993)^2 - (992)^2 + 5 \times 47 + (93)^2 - (92)^2
\]

### Step 1: Simplify each difference of squares.
The difference of squares formula is given by:

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

#### For \((993)^2 - (992)^2\):
\[
(993)^2 - (992)^2 = (993 - 992)(993 + 992) = 1 \times 1985 = 1985
\]

#### For \((93)^2 - (92)^2\):
\[
(93)^2 - (92)^2 = (93 - 92)(93 + 92) = 1 \times 185 = 185
\]

### Step 2: Simplify the expression.
Now we can substitute the simplified values back into the original expression:

\[
1985 + 5 \times 47 + 185
\]

### Step 3: Calculate \(5 \times 47\):
\[
5 \times 47 = 235
\]

### Step 4: Add the results together:
\[
1985 + 235 + 185 = 2405
\]

So, the final value of the expression is:

\[
\boxed{2405}
\]

Do you want any further details or have any questions about this solution?

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Here are five related questions you might find interesting:
1. What is the difference of squares formula used for in algebra?
2. How would the result change if the original numbers were cubed instead of squared?
3. Can you derive a general formula for the sum of two consecutive squares?
4. How does the difference of squares relate to factoring polynomials?
5. What are some practical applications of the difference of squares in real-world scenarios?

**Tip:** Always look out for patterns, like the difference of squares, to simplify complex expressions quickly.

Learn how to simplify and solve the mathematical expression (993)^2 - (992)^2 + 5 * 47 + (93)^2 - (92)^2 step-by-step with a detailed solution. This problem involves algebraic concepts such as the difference of squares formula and arithmetic operations. Suitable for students in Grades 7-9.

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