Simplify algebraic expressions using the distributive property.

To solve the given problems using the distributive property, we will simplify each expression step by step. The distributive property states that \( a(b + c) = ab + ac \). Let's go through each problem:

---

Problem 1: Simplify \(-2(-4x + 5) + 6x\)

1. Distribute \(-2\) across \((-4x + 5)\):
\[
-2(-4x + 5) = (-2)(-4x) + (-2)(5) = 8x - 10
\]
2. Add \(6x\) to the result:
\[
8x - 10 + 6x = (8x + 6x) - 10 = 14x - 10
\]

Answer:
\[
\boxed{14x - 10}
\]

---

Problem 2: Simplify \(7x + 3(-2x + 3)\)

1. Distribute \(3\) across \((-2x + 3)\):
\[
3(-2x + 3) = 3(-2x) + 3(3) = -6x + 9
\]
2. Add \(7x\) to the result:
\[
7x + (-6x + 9) = 7x - 6x + 9 = x + 9
\]

Answer:
\[
\boxed{x + 9}
\]

---

Problem 3: Simplify \(5(-3x + 7) + 5(x - 1)\)

1. Distribute \(5\) across \((-3x + 7)\):
\[
5(-3x + 7) = 5(-3x) + 5(7) = -15x + 35
\]
2. Distribute \(5\) across \((x - 1)\):
\[
5(x - 1) = 5(x) + 5(-1) = 5x - 5
\]
3. Combine the results:
\[
(-15x + 35) + (5x - 5) = -15x + 5x + 35 - 5 = -10x + 30
\]

Answer:
\[
\boxed{-10x + 30}
\]

---

Problem 4: Simplify \(-9(1 - 10x) - 2(3x + 9)\)

1. Distribute \(-9\) across \((1 - 10x)\):
\[
-9(1 - 10x) = -9(1) + (-9)(-10x) = -9 + 90x
\]
2. Distribute \(-2\) across \((3x + 9)\):
\[
-2(3x + 9) = -2(3x) + (-2)(9) = -6x - 18
\]
3. Combine the results:
\[
(-9 + 90x) + (-6x - 18) = -9 - 18 + 90x - 6x = -27 + 84x
\]

Answer:
\[
\boxed{84x - 27}
\]

---

Problem 5: Simplify \(4(2m + 3) + 6m + 5\)

1. Distribute \(4\) across \((2m + 3)\):
\[
4(2m + 3) = 4(2m) + 4(3) = 8m + 12
\]
2. Add \(6m + 5\) to the result:
\[
(8m + 12) + 6m + 5 = 8m + 6m + 12 + 5 = 14m + 17
\]

Answer:
\[
\boxed{14m + 17}
\]

---

Problem 6: Simplify \(6y - (y + 5y) + 3y\)

1. Simplify the term \(-(y + 5y)\):
\[
-(y + 5y) = -y - 5y = -6y
\]
2. Combine all terms:
\[
6y - 6y + 3y = (6y - 6y) + 3y = 0 + 3y = 3y
\]

Answer:
\[
\boxed{3y}
\]

---

Problem 7: Simplify \(7 - 8(-2 - 5x)\)

1. Distribute \(-8\) across \((-2 - 5x)\):
\[
-8(-2 - 5x) = -8(-2) + (-8)(-5x) = 16 + 40x
\]
2. Add \(7\) to the result:
\[
7 + (16 + 40x) = 7 + 16 + 40x = 23 + 40x
\]

Answer:
\[
\boxed{40x + 23}
\]

---

Problem 8: Simplify \(-9x(-9 + 6x) - 5x(7 + 4x)\)

1. Distribute \(-9x\) across \((-9 + 6x)\):
\[
-9x(-9 + 6x) = -9x(-9) + (-9x)(6x) = 81x - 54x^2
\]
2. Distribute \(-5x\) across \((7 + 4x)\):
\[
-5x(7 + 4x) = -5x(7) + (-5x)(4x) = -35x - 20x^2
\]
3. Combine the results:
\[
(81x - 54x^2) + (-35x - 20x^2) = 81x - 35x - 54x^2 - 20x^2 = 46x - 74x^2
\]

Answer:
\[
\boxed{-74x^2 + 46x}
\]

---

Problem 9: Simplify \(-p - 5(-6 - 7p)\)

1. Distribute \(-5\) across \((-6 - 7p)\):
\[
-5(-6 - 7p) = -5(-6) + (-5)(-7p) = 30 + 35p
\]
2. Add \(-p\) to the result:
\[
-p + (30 + 35p) = -p + 35p + 30 = 34p + 30
\]

Answer:
\[
\boxed{34p + 30}
\]

---

Problem 10: Simplify \(-4(1 - 8x) - 9(-10x - 1)\)

1. Distribute \(-4\) across \((1 - 8x)\):
\[
-4(1 - 8x) = -4(1) + (-4)(-8x) = -4 + 32x
\]
2. Distribute \(-9\) across \((-10x - 1)\):
\[
-9(-10x - 1) = -9(-10x) + (-9)(-1) = 90x + 9
\]
3. Combine the results:
\[
(-4 + 32x) + (90x + 9) = -4 + 9 + 32x + 90x = 5 + 122x
\]

Answer:
\[
\boxed{122x + 5}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 14x - 10 \\
2. & \ x + 9 \\
3. & \ -10x + 30 \\
4. & \ 84x - 27 \\
5. & \ 14m + 17 \\
6. & \ 3y \\
7. & \ 40x + 23 \\
8. & \ -74x^2 + 46x \\
9. & \ 34p + 30 \\
10. & \ 122x + 5
\end{aligned}
}
\]