Let's work through the problems presented in the image step by step.

1. Expand and simplify:

   Part b: $7(2x + 3z - y)$

   To expand, multiply each term inside the parentheses by 7: $7(2x + 3z - y) = 7 \cdot 2x + 7 \cdot 3z - 7 \cdot y$ This gives: $14x + 21z - 7y$

2. Expand and simplify:

   Part f: $-(x - 3)$

   Distribute the negative sign (or -1) to each term inside the parentheses: $-(x - 3) = -x + 3$

3. Expand and simplify:

   Part d: $-x(2x + 4)$

   Distribute $-x$ to each term inside the parentheses: $-x(2x + 4) = -x \cdot 2x - x \cdot 4$ This simplifies to: $-2x^2 - 4x$

So, the simplified expressions are:

• $14x + 21z - 7y$
• $-x + 3$
• $-2x^2 - 4x$

Let me know if you need any further clarification or if you'd like to work through more problems!

Further questions to explore:

1. What are the steps for expanding expressions with multiple variables?
2. How do you handle terms with negative signs in parentheses when expanding?
3. Can you factor the expressions you've simplified?
4. What is the difference between expanding and simplifying algebraic expressions?
5. How would you deal with more complex terms involving fractions or exponents?

Tip: Always distribute carefully when you have parentheses, especially with negative signs or coefficients. Double-check each term as you multiply.