Question

Use the distributive property to simplify each expression

-8(x + 4)

12 - (x + 9)

2 (5x - 6)

3 (4x + 1) - 10x

Answer 1

To simplify each expression using the distributive property, we will distribute the factor outside the parentheses to each term inside the parentheses. Let's simplify each expression one by one:

1. **-8(x + 4)**:
\[
-8(x) + (-8)(4) = -8x - 32
\]

2. **12 - (x + 9)**:
\[
12 - x - 9 = 12 - 9 - x = 3 - x
\]

3. **2(5x - 6)**:
\[
2(5x) + 2(-6) = 10x - 12
\]

4. **3(4x + 1) - 10x**:
First, apply the distributive property:
\[
3(4x) + 3(1) = 12x + 3
\]
Now, combine with \(-10x\):
\[
12x + 3 - 10x = (12x - 10x) + 3 = 2x + 3
\]

Now, combining the results, we have:
1. \(-8x - 32\)
2. \(3 - x\)
3. \(10x - 12\)
4. \(2x + 3\)