Question

write an equivalent expression.
3z - 12
select all that apply.
a. (z - 4)3
b. 3(3z - 4)
c. 3(z - 4)
d. 3(z - 12)
click to select your answer(s) and then click check answer.
all parts showing

Explanation:

Step1: Factor the original expression

The original expression is \(3z - 12\). We can factor out the greatest common factor, which is 3. So, \(3z-12 = 3(z - 4)\).

Step2: Analyze Option A

For option A: \((z - 4)3\). Multiplication is commutative, so \((z - 4)3=3(z - 4)\), which is equivalent to the factored form of \(3z - 12\).

Step3: Analyze Option B

For option B: \(3(3z - 4)=9z - 12\), which is not equivalent to \(3z - 12\).

Step4: Analyze Option C

For option C: \(3(z - 4)\), which is the factored form we found in Step 1, so it is equivalent to \(3z - 12\).

Step5: Analyze Option D

For option D: \(3(z - 12)=3z - 36\), which is not equivalent to \(3z - 12\).

Answer:

A. \((z - 4)3\), C. \(3(z - 4)\)