Simplify the following by collecting like terms: 9x + 4y - 5x + 5 2y2 + 6y - y2 - 2y + 8 Expand and then simplify: p2 + 3p(p + 2q + 5r)

$$9x + 4y - 5x + 5$$

The like terms are $9x$ and $-5x$.

$$(9x - 5x) + 4y + 5$$ $$4x + 4y + 5$$

The simplified expression is $\boxed{\text{4x + 4y + 5}}$.

b)

$$2y^2 + 6y - y^2 - 2y + 8$$

The like terms are $2y^2$ and $-y^2$, and $6y$ and $-2y$.

$$y^2 + 4y + 8$$

The simplified expression is \boxed{\text{y^2 + 4y + 8}}.

3. a)

$$3p(p + 2q + 5r) = (3p \times p) + (3p \times 2q) + (3p \times 5r)$$ $$3p(p + 2q + 5r) = 3p^2 + 6pq + 15pr$$

$$p^2 + 3p^2 + 6pq + 15pr$$ $$(p^2 + 3p^2) + 6pq + 15pr$$ $$4p^2 + 6pq + 15pr$$

The expanded and simplified expression is \boxed{\text{4p^2 + 6pq + 15pr}}.