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Еренхий үржигдэхүүнийг хаалтын өмнө гаргаж, тэнцэтгэлийг батал.

The image you've uploaded contains two mathematical expressions. The instruction appears to be in Mongolian, and it says: "Еренхий үржигдэхүүнийг хаалтын өмнө гаргаж, тэнцэтгэлийг батал." This translates to: "Factor out the common factor before the parentheses and verify the equation."

Let’s analyze and solve both parts:

### a. 
\[
\frac{76 + 75 - 74}{11} = 5 \times 74
\]

**Step 1: Simplify the numerator.**  
\[ 76 + 75 - 74 = 77 \]

So, the equation becomes:
\[
\frac{77}{11} = 5 \times 74
\]

**Step 2: Simplify both sides.**  
The left side becomes:
\[
\frac{77}{11} = 7
\]

The right side is:
\[
5 \times 74 = 370
\]

This equation is not valid as \( 7 \neq 370 \), suggesting there could be a typo or error in the problem. Would you like me to review further or attempt a different approach?

---

### b. 
\[
\frac{8^{10} - 8^9 - 8^8}{55} = 8^8
\]

**Step 1: Factor out the common term**  
From the numerator, we can factor out \( 8^8 \):
\[
8^8(8^2 - 8 - 1)
\]

Now, the equation becomes:
\[
\frac{8^8(8^2 - 8 - 1)}{55} = 8^8
\]

**Step 2: Simplify**  
Divide both sides by \( 8^8 \):
\[
\frac{8^2 - 8 - 1}{55} = 1
\]

**Step 3: Solve for the remaining expression**  
Calculate \( 8^2 - 8 - 1 \):
\[
64 - 8 - 1 = 55
\]

So, the equation becomes:
\[
\frac{55}{55} = 1
\]

This simplifies to \( 1 = 1 \), which is true.

Thus, the second equation is valid.

---

Would you like further details or have any questions about the solutions?

Here are 5 related questions:
1. How can you simplify algebraic expressions involving powers?
2. What are common methods for factoring polynomials?
3. Why do we factor out the greatest common divisor in algebraic equations?
4. How do you identify errors or potential typos in equations?
5. Can you explain the process of verifying an equation step by step?

**Tip:** Always check if you can factor out terms to simplify complex equations quickly.

This problem focuses on factoring the common factor before parentheses and verifying the algebraic equation. It includes concepts like powers of 8 and algebraic simplifications. Suitable for students in Grades 10-12.

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