Algebra worksheet focusing on simplifying expressions using the distributive property.

Let's solve each expression step by step using the distributive property, which states:

> $ a(b + c) = ab + ac $

We'll simplify each expression by distributing, combining like terms, and simplifying.

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1. $-2(-4x + 5) + 6x$

Distribute $-2$:
$$
-2 \cdot (-4x) + (-2) \cdot 5 = 8x - 10
$$
Now add $6x$:
$$
8x - 10 + 6x = (8x + 6x) - 10 = 14x - 10
$$

✔ Answer: $ \boxed{14x - 10} $

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2. $7x + 3(-2x + 3)$

Distribute $3$:
$$
3 \cdot (-2x) + 3 \cdot 3 = -6x + 9
$$
Now combine with $7x$:
$$
7x - 6x + 9 = x + 9
$$

✔ Answer: $ \boxed{x + 9} $

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3. $5(-3x + 7) + 5(x - 1)$

Distribute both:
- $5(-3x + 7) = -15x + 35$
- $5(x - 1) = 5x - 5$

Now add:
$$
-15x + 35 + 5x - 5 = (-15x + 5x) + (35 - 5) = -10x + 30
$$

✔ Answer: $ \boxed{-10x + 30} $

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4. $-9(1 - 10x) - 2(3x + 9)$

Distribute:
- $-9(1 - 10x) = -9 + 90x$
- $-2(3x + 9) = -6x - 18$

Now combine:
$$
-9 + 90x - 6x - 18 = (90x - 6x) + (-9 - 18) = 84x - 27
$$

✔ Answer: $ \boxed{84x - 27} $

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5. $4(2m + 3) + 6m + 5$

Distribute:
$$
4 \cdot 2m + 4 \cdot 3 = 8m + 12
$$
Now add:
$$
8m + 12 + 6m + 5 = (8m + 6m) + (12 + 5) = 14m + 17
$$

✔ Answer: $ \boxed{14m + 17} $

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6. $6y - (y + 5y) + 3y$

First simplify inside parentheses:
$$
y + 5y = 6y
$$
So expression becomes:
$$
6y - 6y + 3y = (6y - 6y) + 3y = 0 + 3y = 3y
$$

✔ Answer: $ \boxed{3y} $

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7. $7 - 8(-2 - 5x)$

Distribute $-8$:
$$
-8 \cdot (-2) + (-8) \cdot (-5x) = 16 + 40x
$$
Now add $7$:
$$
7 + 16 + 40x = 23 + 40x
$$

✔ Answer: $ \boxed{40x + 23} $

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8. $-9x(-9 + 6x) - 5x(7 + 4x)$

Distribute each term:

First: $-9x(-9 + 6x) = (-9x)(-9) + (-9x)(6x) = 81x - 54x^2$

Second: $-5x(7 + 4x) = (-5x)(7) + (-5x)(4x) = -35x - 20x^2$

Now combine:
$$
81x - 54x^2 - 35x - 20x^2 = (-54x^2 - 20x^2) + (81x - 35x) = -74x^2 + 46x
$$

✔ Answer: $ \boxed{-74x^2 + 46x} $

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9. $-p - 5(-6 - 7p)$

Distribute $-5$:
$$
-5 \cdot (-6) + (-5) \cdot (-7p) = 30 + 35p
$$
Now combine with $-p$:
$$
-p + 30 + 35p = (-p + 35p) + 30 = 34p + 30
$$

✔ Answer: $ \boxed{34p + 30} $

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10. $-4(1 - 8x) - 9(-10x - 1)$

Distribute:

First: $-4(1 - 8x) = -4 + 32x$

Second: $-9(-10x - 1) = 90x + 9$

Now combine:
$$
-4 + 32x + 90x + 9 = (32x + 90x) + (-4 + 9) = 122x + 5
$$

✔ Answer: $ \boxed{122x + 5} $

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✔ Final Answers Summary:

| Problem | Simplified Expression |
|--------|------------------------|
| 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 | $122x + 5$ |

Let me know if you'd like these explained in video format or need practice problems!