Question

which expression is equivalent to (-24) – 32n? a -8(3 – 4n) b 8(3 + 4n) c -8(3 + 4n) d 8(3 – 4n)

Explanation:

Step1: Factor out -8 from the expression

We start with the expression \(-24 - 32n\). We can factor out \(-8\) from both terms.
For the first term, \(\frac{-24}{-8}=3\), and for the second term, \(\frac{-32n}{-8} = 4n\).
So, factoring out \(-8\) gives us \(-8(3 + 4n)\).

Step2: Check the options

• Option A: \(-8(3 - 4n)=-24 + 32n\), which is not equivalent to \(-24-32n\).
• Option B: \(8(3 + 4n)=24 + 32n\), which is not equivalent.
• Option C: \(-8(3 + 4n)=-24-32n\), which matches our factored form.
• Option D: \(8(3 - 4n)=24 - 32n\), which is not equivalent.

Answer:

C. \(-8(3 + 4n)\)