Practice worksheet featuring ten algebra problems designed to help students master simplifying expressions.

Here are the step-by-step solutions for each problem on the worksheet. I will simplify each expression by using the distributive property (multiplying the number outside the parentheses by each term inside) and then combining like terms.

1.) $-4(3x - 3) + 9(x + 1)$
* Distribute $-4$: $-12x + 12$
* Distribute $9$: $+ 9x + 9$
* Combine: $(-12x + 9x) + (12 + 9)$
* Result: $-3x + 21$

2.) $-9x(5x + 4) + 10(x + 3)$
* Distribute $-9x$: $-45x^2 - 36x$
* Distribute $10$: $+ 10x + 30$
* Combine: $-45x^2 + (-36x + 10x) + 30$
* Result: $-45x^2 - 26x + 30$

3.) $n(1 + 10n) - n(4n - 3)$
* Distribute first $n$: $n + 10n^2$
* Distribute second $-n$: $-4n^2 + 3n$ (Watch the signs! $-n \cdot -3 = +3n$)
* Combine: $(10n^2 - 4n^2) + (n + 3n)$
* Result: $6n^2 + 4n$

4.) $-2n(-8n - 10) - 6(-10n - 3)$
* Distribute $-2n$: $16n^2 + 20n$
* Distribute $-6$: $+ 60n + 18$ (Watch the signs! $-6 \cdot -10n = +60n$ and $-6 \cdot -3 = +18$)
* Combine: $16n^2 + (20n + 60n) + 18$
* Result: $16n^2 + 80n + 18$

5.) $8(-4x - 7) + 3(9 - 9x)$
* Distribute $8$: $-32x - 56$
* Distribute $3$: $+ 27 - 27x$
* Combine: $(-32x - 27x) + (-56 + 27)$
* Result: $-59x - 29$

6.) $9(3 - 10n) - 3(10n + 1)$
* Distribute $9$: $27 - 90n$
* Distribute $-3$: $-30n - 3$
* Combine: $(-90n - 30n) + (27 - 3)$
* Result: $-120n + 24$

7.) $-4(1 - 8x) - 9(-10x - 1)$
* Distribute $-4$: $-4 + 32x$
* Distribute $-9$: $+ 90x + 9$ (Watch the signs! $-9 \cdot -10x = +90x$ and $-9 \cdot -1 = +9$)
* Combine: $(32x + 90x) + (-4 + 9)$
* Result: $122x + 5$

8.) $-9x(-9 + 6x) - 5x(7 + 4x)$
* Distribute $-9x$: $81x - 54x^2$
* Distribute $-5x$: $-35x - 20x^2$
* Combine: $(-54x^2 - 20x^2) + (81x - 35x)$
* Result: $-74x^2 + 46x$

9.) $-4(n + 6) - (1 + 2n)$
* Distribute $-4$: $-4n - 24$
* Distribute the negative sign (same as multiplying by $-1$): $-1 - 2n$
* Combine: $(-4n - 2n) + (-24 - 1)$
* Result: $-6n - 25$

10.) $-2(x + 9) - 4x(3 - 2x)$
* Distribute $-2$: $-2x - 18$
* Distribute $-4x$: $-12x + 8x^2$ (Watch the signs! $-4x \cdot -2x = +8x^2$)
* Combine: $8x^2 + (-2x - 12x) - 18$
* Result: $8x^2 - 14x - 18$

Final Answer:
1.) $-3x + 21$
2.) $-45x^2 - 26x + 30$
3.) $6n^2 + 4n$
4.) $16n^2 + 80n + 18$
5.) $-59x - 29$
6.) $-120n + 24$
7.) $122x + 5$
8.) $-74x^2 + 46x$
9.) $-6n - 25$
10.) $8x^2 - 14x - 18$