Which expressions are equivalent to
\[-6(b+2)+8\] ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
\[-6b+2+8\]
A
\[-6b+2+8\]
(Choice B)
\[-6b-4\]
B
\[-6b-4\]
(Choice C) None of the above
C
None of the above
To simplify the expression \[-6(b+2)+8\], we need to distribute the -6 to both terms inside the parentheses:
\[-6(b+2)+8 = -6b - 12 + 8\]
Simplifying further, we combine like terms:
\[-6b - 12 + 8 = -6b - 4\]
So, the expression \[-6(b+2)+8\] is equivalent to \[-6b - 4\]. Therefore, the answer is (Choice B) \[-6b-4\].
To find the expressions that are equivalent to \(-6(b+2)+8\), we need to simplify the given expression using the distributive property and then combine like terms.
Using the distributive property, we multiply -6 by each term inside the parentheses:
\(-6(b+2) = -6 \cdot b + (-6) \cdot 2\)
This simplifies to:
\(-6b - 12 + 8\)
Now, we can combine like terms:
\(-6b - 4\)
So, the equivalent expression is \(-6b - 4\).
Comparing this with the choices given:
Choice A: \(-6b + 2 + 8\)
This expression includes the constant terms 2 and 8, which are not present in the original expression. Therefore, this choice is not equivalent.
Choice B: \(-6b - 4\)
This expression is the same as the simplified expression we found: \(-6b - 4\). Therefore, this choice is equivalent.
Choice C: None of the above
Since we showed that Choice B is equivalent to the given expression, Choice C is incorrect.
So, the correct answer is:
Choice B: \(-6b - 4\)
The given expression is \(-6(b+2)+8\).
To simplify this expression, we can distribute the -6 to both terms inside the parentheses:
\(-6 \cdot b - 6 \cdot 2 + 8\)
This simplifies to:
\(-6b - 12 + 8\)
Next, we combine like terms:
\(-6b - 4\)
Therefore, the expression is equivalent to \(-6b - 4\).
So the correct answer is (Choice B) \(-6b - 4\). None of the other answer choices are equivalent to the given expression.