Which expressions are equivalent to
\[-2(2h+10)+4h\] ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
\[-20-4h+4h\]
A
\[-20-4h+4h\]
(Choice B)
\[-20\]
B
\[-20\]
(Choice C) None of the above
C
None of the above
The expression \(-2(2h+10)+4h\) can be simplified as follows:
Distribute the \(-2\) to the terms inside the parentheses:
\(-4h - 20 + 4h\)
Combine the like terms \(-4h\) and \(4h\):
\(-20\)
Therefore, the equivalent expression is \(-20\).
So, the correct answers are:
B) \(-20\)
C) None of the above
To determine which expressions are equivalent to \[-2(2h+10)+4h\], we can simplify the given expression step by step.
Step 1: Distribute the -2 to the terms inside the parentheses:
\[ -2 \cdot 2h + (-2) \cdot 10 + 4h \]
Simplifying this, we get:
\[ -4h - 20 + 4h \]
Step 2: Combine like terms:
\[ (-4h + 4h) - 20 \]
The terms \(-4h\) and \(4h\) cancel each other out, leaving us with \(-20\). Therefore, the simplified expression is \[-20\].
Now let's analyze the answer choices:
Choice A: \(-20 - 4h + 4h\)
In this expression, we have the term \(-20\) followed by \(-4h\) and then \(4h\). Notice that \(4h\) and \(-4h\) are additive inverses, meaning they cancel each other out. Thus, this expression simplifies to \(-20\), which is equivalent to the given expression. Therefore, Choice A is correct.
Choice B: \(-20\)
This is the simplified version of the given expression that we obtained earlier. It is equivalent to the given expression. Therefore, Choice B is correct.
Choice C: None of the above
Since both Choice A and Choice B are correct, this choice is incorrect.
Therefore, the correct choices are:
- Choice A: \[-20 - 4h + 4h\]
- Choice B: \[-20\]
The correct answers are:
(Choice A)
\[-20-4h+4h\]
(Choice B)
\[-20\]
So the expressions that are equivalent to \[-2(2h+10)+4h\] are \[-20-4h+4h\] and \[-20\].