This Algebra 1 review sheet features 25 problems designed to help students practice simplifying expressions using the distributive property.

To solve the given problems, we will use the distributive property and simplify each expression step by step. The distributive property states:

\[
a(b + c) = ab + ac
\]

Let's go through each problem systematically.

---

Problem 1: \( 3(5n + 2) - 4n \)

1. Distribute \( 3 \) across \( (5n + 2) \):
\[
3(5n + 2) = 3 \cdot 5n + 3 \cdot 2 = 15n + 6
\]
2. Subtract \( 4n \):
\[
15n + 6 - 4n = (15n - 4n) + 6 = 11n + 6
\]

Answer:
\[
\boxed{11n + 6}
\]

---

Problem 2: \( 8 + 7(4 + 2b) \)

1. Distribute \( 7 \) across \( (4 + 2b) \):
\[
7(4 + 2b) = 7 \cdot 4 + 7 \cdot 2b = 28 + 14b
\]
2. Add \( 8 \):
\[
8 + 28 + 14b = 36 + 14b
\]

Answer:
\[
\boxed{36 + 14b}
\]

---

Problem 3: \( 2(1 - 9v) - 9v \)

1. Distribute \( 2 \) across \( (1 - 9v) \):
\[
2(1 - 9v) = 2 \cdot 1 + 2 \cdot (-9v) = 2 - 18v
\]
2. Subtract \( 9v \):
\[
2 - 18v - 9v = 2 - 27v
\]

Answer:
\[
\boxed{2 - 27v}
\]

---

Problem 4: \( 8x - 7(x + 7) \)

1. Distribute \( -7 \) across \( (x + 7) \):
\[
-7(x + 7) = -7 \cdot x + (-7) \cdot 7 = -7x - 49
\]
2. Combine with \( 8x \):
\[
8x - 7x - 49 = (8x - 7x) - 49 = x - 49
\]

Answer:
\[
\boxed{x - 49}
\]

---

Problem 5: \( -8(6 - 7n) + 5n \)

1. Distribute \( -8 \) across \( (6 - 7n) \):
\[
-8(6 - 7n) = -8 \cdot 6 + (-8) \cdot (-7n) = -48 + 56n
\]
2. Add \( 5n \):
\[
-48 + 56n + 5n = -48 + 61n
\]

Answer:
\[
\boxed{-48 + 61n}
\]

---

Problem 6: \( 4 - 4(-6a - 7) \)

1. Distribute \( -4 \) across \( (-6a - 7) \):
\[
-4(-6a - 7) = -4 \cdot (-6a) + (-4) \cdot (-7) = 24a + 28
\]
2. Subtract from \( 4 \):
\[
4 + 24a + 28 = 24a + 32
\]

Answer:
\[
\boxed{24a + 32}
\]

---

Problem 7: \( -4(-20 + 7k) + 6(-9 - k) \)

1. Distribute \( -4 \) across \( (-20 + 7k) \):
\[
-4(-20 + 7k) = -4 \cdot (-20) + (-4) \cdot 7k = 80 - 28k
\]
2. Distribute \( 6 \) across \( (-9 - k) \):
\[
6(-9 - k) = 6 \cdot (-9) + 6 \cdot (-k) = -54 - 6k
\]
3. Combine the results:
\[
80 - 28k - 54 - 6k = (80 - 54) + (-28k - 6k) = 26 - 34k
\]

Answer:
\[
\boxed{26 - 34k}
\]

---

Problem 8: \( -17(1 + 16p) + 3(15p - 10) \)

1. Distribute \( -17 \) across \( (1 + 16p) \):
\[
-17(1 + 16p) = -17 \cdot 1 + (-17) \cdot 16p = -17 - 272p
\]
2. Distribute \( 3 \) across \( (15p - 10) \):
\[
3(15p - 10) = 3 \cdot 15p + 3 \cdot (-10) = 45p - 30
\]
3. Combine the results:
\[
-17 - 272p + 45p - 30 = (-17 - 30) + (-272p + 45p) = -47 - 227p
\]

Answer:
\[
\boxed{-47 - 227p}
\]

---

Problem 9: \( -14(7x - 9) - 19(x - 3) \)

1. Distribute \( -14 \) across \( (7x - 9) \):
\[
-14(7x - 9) = -14 \cdot 7x + (-14) \cdot (-9) = -98x + 126
\]
2. Distribute \( -19 \) across \( (x - 3) \):
\[
-19(x - 3) = -19 \cdot x + (-19) \cdot (-3) = -19x + 57
\]
3. Combine the results:
\[
-98x + 126 - 19x + 57 = (-98x - 19x) + (126 + 57) = -117x + 183
\]

Answer:
\[
\boxed{-117x + 183}
\]

---

Problem 10: \( 7(n + 20) + 13(1 - 20n) \)

1. Distribute \( 7 \) across \( (n + 20) \):
\[
7(n + 20) = 7 \cdot n + 7 \cdot 20 = 7n + 140
\]
2. Distribute \( 13 \) across \( (1 - 20n) \):
\[
13(1 - 20n) = 13 \cdot 1 + 13 \cdot (-20n) = 13 - 260n
\]
3. Combine the results:
\[
7n + 140 + 13 - 260n = (7n - 260n) + (140 + 13) = -253n + 153
\]

Answer:
\[
\boxed{-253n + 153}
\]

---

Problem 11: \( 16(2 - 7m) - 8(5m + 3) \)

1. Distribute \( 16 \) across \( (2 - 7m) \):
\[
16(2 - 7m) = 16 \cdot 2 + 16 \cdot (-7m) = 32 - 112m
\]
2. Distribute \( -8 \) across \( (5m + 3) \):
\[
-8(5m + 3) = -8 \cdot 5m + (-8) \cdot 3 = -40m - 24
\]
3. Combine the results:
\[
32 - 112m - 40m - 24 = (32 - 24) + (-112m - 40m) = 8 - 152m
\]

Answer:
\[
\boxed{8 - 152m}
\]

---

Problem 12: \( -4(1 - r) - 11(9r - 6) \)

1. Distribute \( -4 \) across \( (1 - r) \):
\[
-4(1 - r) = -4 \cdot 1 + (-4) \cdot (-r) = -4 + 4r
\]
2. Distribute \( -11 \) across \( (9r - 6) \):
\[
-11(9r - 6) = -11 \cdot 9r + (-11) \cdot (-6) = -99r + 66
\]
3. Combine the results:
\[
-4 + 4r - 99r + 66 = (-4 + 66) + (4r - 99r) = 62 - 95r
\]

Answer:
\[
\boxed{62 - 95r}
\]

---

Problem 13: \( 5(x - 1) - 15(x + 17) \)

1. Distribute \( 5 \) across \( (x - 1) \):
\[
5(x - 1) = 5 \cdot x + 5 \cdot (-1) = 5x - 5
\]
2. Distribute \( -15 \) across \( (x + 17) \):
\[
-15(x + 17) = -15 \cdot x + (-15) \cdot 17 = -15x - 255
\]
3. Combine the results:
\[
5x - 5 - 15x - 255 = (5x - 15x) + (-5 - 255) = -10x - 260
\]

Answer:
\[
\boxed{-10x - 260}
\]

---

Problem 14: \( -10(1 - 4n) + 8(n + 15) \)

1. Distribute \( -10 \) across \( (1 - 4n) \):
\[
-10(1 - 4n) = -10 \cdot 1 + (-10) \cdot (-4n) = -10 + 40n
\]
2. Distribute \( 8 \) across \( (n + 15) \):
\[
8(n + 15) = 8 \cdot n + 8 \cdot 15 = 8n + 120
\]
3. Combine the results:
\[
-10 + 40n + 8n + 120 = (-10 + 120) + (40n + 8n) = 110 + 48n
\]

Answer:
\[
\boxed{110 + 48n}
\]

---

Problem 15: \( 5(3b + 6) - 2(1 - 2b) \)

1. Distribute \( 5 \) across \( (3b + 6) \):
\[
5(3b + 6) = 5 \cdot 3b + 5 \cdot 6 = 15b + 30
\]
2. Distribute \( -2 \) across \( (1 - 2b) \):
\[
-2(1 - 2b) = -2 \cdot 1 + (-2) \cdot (-2b) = -2 + 4b
\]
3. Combine the results:
\[
15b + 30 - 2 + 4b = (15b + 4b) + (30 - 2) = 19b + 28
\]

Answer:
\[
\boxed{19b + 28}
\]

---

Problem 16: \( -16(-19v + 8) + 7(-20v - 11) \)

1. Distribute \( -16 \) across \( (-19v + 8) \):
\[
-16(-19v + 8) = -16 \cdot (-19v) + (-16) \cdot 8 = 304v - 128
\]
2. Distribute \( 7 \) across \( (-20v - 11) \):
\[
7(-20v - 11) = 7 \cdot (-20v) + 7 \cdot (-11) = -140v - 77
\]
3. Combine the results:
\[
304v - 128 - 140v - 77 = (304v - 140v) + (-128 - 77) = 164v - 205
\]

Answer:
\[
\boxed{164v - 205}
\]

---

Problem 17: \( 14(18 + 11x) + 3(11 - 20x) \)

1. Distribute \( 14 \) across \( (18 + 11x) \):
\[
14(18 + 11x) = 14 \cdot 18 + 14 \cdot 11x = 252 + 154x
\]
2. Distribute \( 3 \) across \( (11 - 20x) \):
\[
3(11 - 20x) = 3 \cdot 11 + 3 \cdot (-20x) = 33 - 60x
\]
3. Combine the results:
\[
252 + 154x + 33 - 60x = (252 + 33) + (154x - 60x) = 285 + 94x
\]

Answer:
\[
\boxed{285 + 94x}
\]

---

Problem 18: \( 13(13 + 14n) - (14 + 12n) \)

1. Distribute \( 13 \) across \( (13 + 14n) \):
\[
13(13 + 14n) = 13 \cdot 13 + 13 \cdot 14n = 169 + 182n
\]
2. Distribute the negative sign across \( (14 + 12n) \):
\[
-(14 + 12n) = -14 - 12n
\]
3. Combine the results:
\[
169 + 182n - 14 - 12n = (169 - 14) + (182n - 12n) = 155 + 170n
\]

Answer:
\[
\boxed{155 + 170n}
\]

---

Problem 19: \( 3(-12a + 17) - 4(18a + 2) \)

1. Distribute \( 3 \) across \( (-12a + 17) \):
\[
3(-12a + 17) = 3 \cdot (-12a) + 3 \cdot 17 = -36a + 51
\]
2. Distribute \( -4 \) across \( (18a + 2) \):
\[
-4(18a + 2) = -4 \cdot 18a + (-4) \cdot 2 = -72a - 8
\]
3. Combine the results:
\[
-36a + 51 - 72a - 8 = (-36a - 72a) + (51 - 8) = -108a + 43
\]

Answer:
\[
\boxed{-108a + 43}
\]

---

Problem 20: \( 4(1 + 17k) - 7(k + 16) \)

1. Distribute \( 4 \) across \( (1 + 17k) \):
\[
4(1 + 17k) = 4 \cdot 1 + 4 \cdot 17k = 4 + 68k
\]
2. Distribute \( -7 \) across \( (k + 16) \):
\[
-7(k + 16) = -7 \cdot k + (-7) \cdot 16 = -7k - 112
\]
3. Combine the results:
\[
4 + 68k - 7k - 112 = (4 - 112) + (68k - 7k) = -108 + 61k
\]

Answer:
\[
\boxed{61k - 108}
\]

---

Problem 21: \( -13(17 - 8x) - 18(-2x + 16) \)

1. Distribute \( -13 \) across \( (17 - 8x) \):
\[
-13(17 - 8x) = -13 \cdot 17 + (-13) \cdot (-8x) = -221 + 104x
\]
2. Distribute \( -18 \) across \( (-2x + 16) \):
\[
-18(-2x + 16) = -18 \cdot (-2x) + (-18) \cdot 16 = 36x - 288
\]
3. Combine the results:
\[
-221 + 104x + 36x - 288 = (-221 - 288) + (104x + 36x) = -509 + 140x
\]

Answer:
\[
\boxed{140x - 509}
\]

---

Problem 22: \( -8(-15x - 18) - 5(-19 + 6x) \)

1. Distribute \( -8 \) across \( (-15x - 18) \):
\[
-8(-15x - 18) = -8 \cdot (-15x) + (-8) \cdot (-18) = 120x + 144
\]
2. Distribute \( -5 \) across \( (-19 + 6x) \):
\[
-5(-19 + 6x) = -5 \cdot (-19) + (-5) \cdot 6x = 95 - 30x
\]
3. Combine the results:
\[
120x + 144 + 95 - 30x = (120x - 30x) + (144 + 95) = 90x + 239
\]

Answer:
\[
\boxed{90x + 239}
\]

---

Problem 23: \( -13(-13k - 9) - (k + 19) \)

1. Distribute \( -13 \) across \( (-13k - 9) \):
\[
-13(-13k - 9) = -13 \cdot (-13k) + (-13) \cdot (-9) = 169k + 117
\]
2. Distribute the negative sign across \( (k + 19) \):
\[
-(k + 19) = -k - 19
\]
3. Combine the results:
\[
169k + 117 - k - 19 = (169k - k) + (117 - 19) = 168k + 98
\]

Answer:
\[
\boxed{168k + 98}
\]

---

Problem 24: \( -11(n - 12) - 12(-5n - 3) \)

1. Distribute \( -11 \) across \( (n - 12) \):
\[
-11(n - 12) = -11 \cdot n + (-11) \cdot (-12) = -11n + 132
\]
2. Distribute \( -12 \) across \( (-5n - 3) \):
\[
-12(-5n - 3) = -12 \cdot (-5n) + (-12) \cdot (-3) = 60n + 36
\]
3. Combine the results:
\[
-11n + 132 + 60n + 36 = (-11n + 60n) + (132 + 36) = 49n + 168
\]

Answer:
\[
\boxed{49n + 168}
\]

---

Problem 25: \( -3(1 + 3p) - 16(1 + p) \)

1. Distribute \( -3 \) across \( (1 + 3p) \):
\[
-3(1 + 3p) = -3 \cdot 1 + (-3) \cdot 3p = -3 - 9p
\]
2. Distribute \( -16 \) across \( (1 + p) \):
\[
-16(1 + p) = -16 \cdot 1 + (-16) \cdot p = -16 - 16p
\]
3. Combine the results:
\[
-3 - 9p - 16 - 16p = (-3 - 16) + (-9p - 16p) = -19 - 25p
\]

Answer:
\[
\boxed{-19 - 25p}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 11n + 6 \\
2. & \ 36 + 14b \\
3. & \ 2 - 27v \\
4. & \ x - 49 \\
5. & \ -48 + 61n \\
6. & \ 24a + 32 \\
7. & \ 26 - 34k \\
8. & \ -47 - 227p \\
9. & \ -117x + 183 \\
10. & \ -253n + 153 \\
11. & \ 8 - 152m \\
12. & \ 62 - 95r \\
13. & \ -10x - 260 \\
14. & \ 110 + 48n \\
15. & \ 19b + 28 \\
16. & \ 164v - 205 \\
17. & \ 285 + 94x \\
18. & \ 155 + 170n \\
19. & \ -108a + 43 \\
20. & \ 61k - 108 \\
21. & \ 140x - 509 \\
22. & \ 90x + 239 \\
23. & \ 168k + 98 \\
24. & \ 49n + 168 \\
25. & \ -19 - 25p \\
\end{aligned}
}
\]