The image shows a mathematics exercise on expanding algebraic expressions. Let’s solve the problems step by step. Here's the detailed process:

1. $a(2 \times a - 5 \times b + c)$

Expand by distributing $a$ to each term inside the parentheses: $a \cdot 2a - a \cdot 5b + a \cdot c = 2a^2 - 5ab + ac$

2. $5a(2 \times a - 7 \times a^2 + ab)$

Distribute $5a$ to each term: $5a \cdot 2a - 5a \cdot 7a^2 + 5a \cdot ab = 10a^2 - 35a^3 + 5a^2b$

3. $-a(4a - b + 7a^2)$

Distribute $-a$ to each term: $-a \cdot 4a - (-a \cdot b) - a \cdot 7a^2 = -4a^2 + ab - 7a^3$

Final Results:

1. $2a^2 - 5ab + ac$
2. $10a^2 - 35a^3 + 5a^2b$
3. $-4a^2 + ab - 7a^3$

Would you like further clarification or explanations for these steps?

Here are some related questions to explore further:

1. What does it mean to factorize an expression instead of expanding it?
2. How can we check our expanded results for correctness?
3. Can these types of expressions be simplified further after expansion?
4. How does the distributive property apply to expressions with more variables?
5. What are common errors when distributing negative signs in algebra?

Tip: Always double-check your results by re-assembling the expression after expansion—it should match the original!