Question

use distributive property to simplify each expression. easy to medium problems.

1. $7(1 - 8n)$
2. $-8(b + 3)$
3. $-6(9 - 9v)$
4. $-(3x - 9)$
5. $-9(n + 6)$
6. $-10(a + 2)$
7. $(5k - 10) \cdot -9$
8. $-4(4 + 3p)$

Explanation:

Problem 1: \( 7(1 - 8n) \)

Step 1: Apply Distributive Property

The distributive property states that \( a(b - c) = ab - ac \). Here, \( a = 7 \), \( b = 1 \), and \( c = 8n \).

$$ 7(1 - 8n) = 7 \times 1 - 7 \times 8n $$

Step 2: Simplify the products

$$ 7 \times 1 = 7 \quad \text{and} \quad 7 \times 8n = 56n $$

So, \( 7(1 - 8n) = 7 - 56n \)

Problem 2: \( -8(b + 3) \)

Step 1: Apply Distributive Property

The distributive property states that \( a(b + c) = ab + ac \). Here, \( a = -8 \), \( b = b \), and \( c = 3 \).

$$ -8(b + 3) = -8 \times b + (-8) \times 3 $$

Step 2: Simplify the products

$$ -8 \times b = -8b \quad \text{and} \quad -8 \times 3 = -24 $$

So, \( -8(b + 3) = -8b - 24 \)

Problem 3: \( -6(9 - 9v) \)

Step 1: Apply Distributive Property

The distributive property states that \( a(b - c) = ab - ac \). Here, \( a = -6 \), \( b = 9 \), and \( c = 9v \).

$$ -6(9 - 9v) = -6 \times 9 - (-6) \times 9v $$

Step 2: Simplify the products

$$ -6 \times 9 = -54 \quad \text{and} \quad -(-6) \times 9v = 54v $$

So, \( -6(9 - 9v) = -54 + 54v \)

Problem 4: \( -(3x - 9) \)

Answer:

s:

1. \( 7 - 56n \)
2. \( -8b - 24 \)
3. \( -54 + 54v \)
4. \( -3x + 9 \)
5. \( -9n - 54 \)
6. \( -10a - 20 \)
7. \( -45k + 90 \)
8. \( -16 - 12p \)