Question

3 a. 12(-7z + 11x + 8)
3 b. -4(-5 + 2x)
4 a. 8(-7s - v)
4 b. -8(9 + 2y)
5 a. -3(9p + 8)
5 b. 10(11z + 1)
6 a. 11(11c + q)
6 b. 7(-7n + 4)
7 a. 7(-7d - 2 + 10w)
7 b. 2(-m - 6 - 2b)

Explanation:

Let's solve these problems one by one using the distributive property \( a(b + c) = ab + ac \).

3a: \( 12(-7z + 11x + 8) \)

Step 1: Distribute 12 to each term

\( 12 \times (-7z) + 12 \times 11x + 12 \times 8 \)

Step 2: Calculate each product

\( -84z + 132x + 96 \)

3b: \( -4(-5 + 2x) \)

Step 1: Distribute -4 to each term

\( -4 \times (-5) + (-4) \times 2x \)

Step 2: Calculate each product

\( 20 - 8x \)

4a: \( 8(-7s - v) \)

Step 1: Distribute 8 to each term

\( 8 \times (-7s) + 8 \times (-v) \)

Step 2: Calculate each product

\( -56s - 8v \)

4b: \( -8(9 + 2y) \)

Step 1: Distribute -8 to each term

\( -8 \times 9 + (-8) \times 2y \)

Step 2: Calculate each product

\( -72 - 16y \)

5a: \( -3(9p + 8) \)

Step 1: Distribute -3 to each term

\( -3 \times 9p + (-3) \times 8 \)

Step 2: Calculate each product

\( -27p - 24 \)

5b: \( 10(11z + 1) \)

Step 1: Distribute 10 to each term

\( 10 \times 11z + 10 \times 1 \)

Step 2: Calculate each product

\( 110z + 10 \)

6a: \( 11(11c + q) \)

Step 1: Distribute 11 to each term

\( 11 \times 11c + 11 \times q \)

Step 2: Calculate each product

\( 121c + 11q \)

6b: \( 7(-7n + 4) \)

Step 1: Distribute 7 to each term

\( 7 \times (-7n) + 7 \times 4 \)

Step 2: Calculate each product

\( -49n + 28 \)

7a: \( 7(-7d - 2 + 10w) \)

Step 1: Distribute 7 to each term

\( 7 \times (-7d) + 7 \times (-2) + 7 \times 10w \)

Step 2: Calculate each product

\( -49d - 14 + 70w \)

7b: \( 2(-m - 6 - 2b) \)

Step 1: Distribute 2 to each term

\( 2 \times (-m) + 2 \times (-6) + 2 \times (-2b) \)

Step 2: Calculate each product

\( -2m - 12 - 4b \)

Answer:

3a: \(-84z + 132x + 96\)
3b: \(20 - 8x\)
4a: \(-56s - 8v\)
4b: \(-72 - 16y\)
5a: \(-27p - 24\)
5b: \(110z + 10\)
6a: \(121c + 11q\)
6b: \(-49n + 28\)
7a: \(-49d - 14 + 70w\)
7b: \(-2m - 12 - 4b\)