Question 8

Find the product:
[tex]\[ 4(3x - 2) \][/tex]

A. [tex]\(12x - 8\)[/tex]

B. [tex]\(64x - 32\)[/tex]

C. [tex]\(-8x + 16\)[/tex]

D. [tex]\(-6x^2 + 18x\)[/tex]



Answer :

Let's solve the problem step by step:

We are asked to find the product of [tex]\( 4(3x - 2) \)[/tex].

### Step 1: Understand the Expression

The given expression is [tex]\( 4(3x - 2) \)[/tex]. This means we need to multiply each term inside the parentheses by [tex]\( 4 \)[/tex].

### Step 2: Distribute the Constant

Distribute the [tex]\( 4 \)[/tex] across the terms inside the parenthesis:

1. Multiply [tex]\( 4 \)[/tex] by [tex]\( 3x \)[/tex]:
[tex]\[ 4 \cdot 3x = 12x \][/tex]
2. Multiply [tex]\( 4 \)[/tex] by [tex]\( -2 \)[/tex]:
[tex]\[ 4 \cdot (-2) = -8 \][/tex]

### Step 3: Combine the Results

After distribution, the terms inside the parentheses have been multiplied by [tex]\( 4 \)[/tex], resulting in:
[tex]\[ 12x - 8 \][/tex]

This is the product of the expression [tex]\( 4(3x - 2) \)[/tex].

### Conclusion

Therefore, the correct answer is [tex]\( 12x - 8 \)[/tex]. Among the given options:

- [tex]\( 12x - 8 \)[/tex]
- [tex]\( 64x - 32 \)[/tex]
- [tex]\( -8x + 16 \)[/tex]
- [tex]\( -6x^2 + 18x \)[/tex]

The correct choice is [tex]\(\boxed{12x - 8}\)[/tex].