Simplify the Expressions worksheet for algebra practice.

Explanation:
We need to simplify each algebraic expression by combining like terms. Like terms are terms that have the same variables raised to the same powers (e.g., $4ax$ and $-5ax$ are like terms because both have $ax$).

Let’s go one by one:

1. $4ax - 5ax + 4$
Combine $4ax - 5ax = -1ax = -ax$.
So: $-ax + 4$

2. $12ax^2 - 8ax^2 + 4$
$12ax^2 - 8ax^2 = 4ax^2$
So: $4ax^2 + 4$

3. $4a^2x - 5a^2x + 4y - 9y$
$4a^2x - 5a^2x = -a^2x$
$4y - 9y = -5y$
So: $-a^2x - 5y$

4. $-3y^2x + 6xy^2 - 2y - 7y$
Note: $-3y^2x$ and $6xy^2$ are the same (multiplication is commutative: $xy^2 = y^2x$), so:
$-3xy^2 + 6xy^2 = 3xy^2$
$-2y - 7y = -9y$
So: $3xy^2 - 9y$

5. $6m^2n^3 - 12mn - 5mn - 8m^2n^3$
Group like terms:
$6m^2n^3 - 8m^2n^3 = -2m^2n^3$
$-12mn - 5mn = -17mn$
So: $-2m^2n^3 - 17mn$

6. $-21mn + 4f - 2f - 5mn$
$-21mn - 5mn = -26mn$
$4f - 2f = 2f$
So: $-26mn + 2f$

7. $7x^2y - xy^2 - 5x^2y - 2xy^2$
$7x^2y - 5x^2y = 2x^2y$
$-xy^2 - 2xy^2 = -3xy^2$
So: $2x^2y - 3xy^2$

8. $3xy + 8yx - 5 + 4$
Note: $yx = xy$, so $3xy + 8xy = 11xy$
$-5 + 4 = -1$
So: $11xy - 1$

9. $10x - 4 + 5 + x$
$10x + x = 11x$
$-4 + 5 = 1$
So: $11x + 1$

10. $-3a^2x^2 + 5a^2x^2 + 4y - 3y$
$-3a^2x^2 + 5a^2x^2 = 2a^2x^2$
$4y - 3y = y$
So: $2a^2x^2 + y$

Now double-check each for errors — all look correct.

Final Answer:
1. $-ax + 4$
2. $4ax^2 + 4$
3. $-a^2x - 5y$
4. $3xy^2 - 9y$
5. $-2m^2n^3 - 17mn$
6. $-26mn + 2f$
7. $2x^2y - 3xy^2$
8. $11xy - 1$
9. $11x + 1$
10. $2a^2x^2 + y$