https://file.aiquickdraw.com/mathbot/file/1726374143550udo09jsa.jpg

The expression in the image is as follows:

\[
\frac{789 \times 789 \times 789 + 211 \times 211 \times 211}{789 \times 789 - 789 \times 211 + 211 \times 211}
\]

Let's solve this step by step:

### Numerator:
\[
789^3 + 211^3
\]
First, calculate the cubes of \(789\) and \(211\):
- \(789^3 = 789 \times 789 \times 789 = 492,399,669\)
- \(211^3 = 211 \times 211 \times 211 = 9,390,331\)

So the numerator is:
\[
492,399,669 + 9,390,331 = 501,790,000
\]

### Denominator:
\[
789^2 - 789 \times 211 + 211^2
\]
Now, calculate each term:
- \(789^2 = 789 \times 789 = 622,521\)
- \(789 \times 211 = 166,479\)
- \(211^2 = 211 \times 211 = 44,521\)

So the denominator becomes:
\[
622,521 - 166,479 + 44,521 = 500,563
\]

### Final Result:
Now, divide the numerator by the denominator:
\[
\frac{501,790,000}{500,563} \approx 1002.45
\]

The value of the given expression is approximately **1002.45**.

Do you want more details on the steps? Here are 5 related questions:
1. How can you simplify expressions involving cubes and squares?
2. What are other efficient methods to calculate large powers manually?
3. How is the distributive property used in breaking down such complex terms?
4. Can this expression be solved using approximation techniques?
5. How do these types of problems appear in algebraic identities?

**Tip:** When solving complex expressions with large numbers, using approximations and factoring techniques can sometimes simplify calculations.

789 × 789 × 789 + 211 × 211 × 211 divided by 789 × 789 - 789 × 211 + 211 × 211

Learn how to solve the complex algebraic expression (789^3 + 211^3) / (789^2 - 789 × 211 + 211^2). This problem covers key mathematical concepts such as cubes, squares, and factorization, suitable for students in Grades 9-11.

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