To expand and simplify the expression [tex]\( 4(2x - 3) - 2(x - 1) \)[/tex], follow these steps:
### Step 1: Distribute the Constants
First, distribute the constants outside the parentheses to each term inside the parentheses.
1. Distribute the 4 in [tex]\( 4(2x - 3) \)[/tex]:
- [tex]\( 4 \times 2x = 8x \)[/tex]
- [tex]\( 4 \times -3 = -12 \)[/tex]
So, [tex]\( 4(2x - 3) \)[/tex] becomes [tex]\( 8x - 12 \)[/tex].
2. Distribute the -2 in [tex]\( -2(x - 1) \)[/tex]:
- [tex]\( -2 \times x = -2x \)[/tex]
- [tex]\( -2 \times -1 = 2 \)[/tex]
So, [tex]\( -2(x - 1) \)[/tex] becomes [tex]\( -2x + 2 \)[/tex].
### Step 2: Combine Like Terms
Now combine all expressions together:
[tex]\[ 8x - 12 - 2x + 2 \][/tex]
Combine the [tex]\( x \)[/tex]-terms:
[tex]\[ 8x - 2x = 6x \][/tex]
Combine the constant terms:
[tex]\[ -12 + 2 = -10 \][/tex]
### Step 3: Write the Simplified Expression
The simplified expression is:
[tex]\[ 6x - 10 \][/tex]
Therefore, the expanded and simplified form of [tex]\( 4(2x - 3) - 2(x - 1) \)[/tex] is:
[tex]\[ 6x - 10 \][/tex]
