Let's break down and expand each of these expressions:

1. Expression C:

$C = 2y(7 + y)$ Distribute the $2y$ across the terms inside the parentheses:

$C = 2y \cdot 7 + 2y \cdot y$ $C = 14y + 2y^2$

2. Expression D:

$D = x(4x - 8)$ Distribute the $x$ across the terms inside the parentheses:

$D = x \cdot 4x - x \cdot 8$ $D = 4x^2 - 8x$

3. Expression E:

$E = -w(w - 2)$ Distribute the $-w$ across the terms inside the parentheses:

$E = -w \cdot w + (-w) \cdot (-2)$ $E = -w^2 + 2w$

4. Expression F:

$F = -2x(5x - 3)$ Distribute the $-2x$ across the terms inside the parentheses:

$F = -2x \cdot 5x + (-2x) \cdot (-3)$ $F = -10x^2 + 6x$

Final Results:

1. $C = 14y + 2y^2$
2. $D = 4x^2 - 8x$
3. $E = -w^2 + 2w$
4. $F = -10x^2 + 6x$

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Would you like to explore any of these in more detail or need further help with other questions?

Here are 5 related questions to deepen understanding:

1. What is the difference between expanding a binomial and factoring one?
2. How do you combine like terms when simplifying algebraic expressions?
3. What does it mean to "distribute" in algebra, and why is it important?
4. How can you factor expressions like $4x^2 - 8x$ or $-w^2 + 2w$?
5. What would the graph of the expression $C = 14y + 2y^2$ look like?

Tip: When expanding expressions like these, it's always helpful to write each step out clearly to avoid missing any terms during the distribution.