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Which expressions are equivalent to [tex]4m - 2 + (-8m)[/tex]?

Choose all answers that apply:

A. [tex]-2(4m + 1) + 4m[/tex]

B. [tex]2(2m - 1) - 8m[/tex]

C. None of the above

Sagot :

GinnyAnsweridn
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)
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