To determine which expressions are equivalent to [tex]\(4m - 2 + (-8m)\)[/tex], let's simplify the given expression and then compare it with the provided options.
### Simplify the Given Expression
[tex]\[4m - 2 + (-8m)\][/tex]
Combine like terms (terms involving [tex]\(m\)[/tex]):
[tex]\[4m + (-8m) - 2\][/tex]
[tex]\[ (4 - 8)m - 2 \][/tex]
[tex]\[ -4m - 2 \][/tex]
The simplified form of the given expression is [tex]\(-4m - 2\)[/tex].
### Evaluate Option (A)
Option (A):
[tex]\[-2(4m + 1) + 4m\][/tex]
First, expand [tex]\(-2(4m + 1)\)[/tex]:
[tex]\[-2 \cdot 4m + (-2) \cdot 1\][/tex]
[tex]\[-8m - 2\][/tex]
Then, add [tex]\(4m\)[/tex]:
[tex]\[-8m - 2 + 4m\][/tex]
Combine the like terms:
[tex]\[ (-8m + 4m) - 2 \][/tex]
[tex]\[ -4m - 2 \][/tex]
Option (A) simplifies to [tex]\(-4m - 2\)[/tex], which matches the simplified form of the given expression.
### Evaluate Option (B)
Option (B):
[tex]\[2(2m - 1) - 8m\][/tex]
First, expand [tex]\(2(2m - 1)\)[/tex]:
[tex]\[ 2 \cdot 2m + 2 \cdot (-1) \][/tex]
[tex]\[ 4m - 2 \][/tex]
Then, subtract [tex]\(8m\)[/tex]:
[tex]\[ 4m - 2 - 8m\][/tex]
Combine the like terms:
[tex]\[ (4m - 8m) - 2 \][/tex]
[tex]\[ -4m - 2 \][/tex]
Option (B) also simplifies to [tex]\(-4m - 2\)[/tex], which matches the simplified form of the given expression.
### Conclusion
Both option (A) and option (B) simplify to the same expression as the given expression [tex]\(-4m - 2\)[/tex].
Hence, the correct answers are:
- (A)
- (B)
