I see the image includes two mathematical expressions:

5. $\left( 4 \sqrt{a}(x-1) \right)^2$
6. $\left( a^3 - 6^3 \right)^2$

Let me solve them step by step:

Problem 5:

Simplify $\left( 4 \sqrt{a}(x-1) \right)^2$.

Solution:

1. Expand the square: $\left( 4 \sqrt{a}(x-1) \right)^2 = \left( 4 \sqrt{a} \right)^2 \cdot (x-1)^2$

2. Calculate $\left( 4 \sqrt{a} \right)^2$: $\left( 4 \sqrt{a} \right)^2 = 16a$

3. Combine results: $\left( 4 \sqrt{a}(x-1) \right)^2 = 16a (x-1)^2$

Final Answer: $16a (x-1)^2$

Problem 6:

Simplify $\left( a^3 - 6^3 \right)^2$.

Solution:

1. Recall the formula for the cube of a number: $6^3 = 216$.
   Substituting this: $\left( a^3 - 6^3 \right)^2 = \left( a^3 - 216 \right)^2$

2. This is already simplified unless more expansion is required.

Final Answer: $\left( a^3 - 216 \right)^2$

Let me know if you want further steps, detailed explanations, or additional examples.

Relative Questions:

1. How do you expand expressions like $(x+y)^2$ or $(x-y)^2$?
2. Can you explain the difference between squaring and taking the square root?
3. How can $a^3 - b^3$ be factored further using the difference of cubes formula?
4. What happens if $a$ is negative or $a = 0$ in these equations?
5. How can this knowledge of expansion apply to physics or engineering problems?

Tip:

When squaring a term with multiple factors, square each factor individually, then multiply them.