Question

write an equivalent expression for 4c + 8. select all that apply. a. (c + 2)4 b. 4(c + 8) c. 4(4c + 2) d. 4(c + 2)

Explanation:

Step1: Factor the original expression

The original expression is \(4c + 8\). We can factor out the greatest common factor, which is 4. So, \(4c+8 = 4(c + 2)\).

Step2: Analyze Option A

Option A is \((c + 2)4\). Multiplication is commutative, so \((c + 2)4=4(c + 2)\), which is equivalent to the original expression.

Step3: Analyze Option B

Option B is \(4(c + 8)\). Using the distributive property, \(4(c + 8)=4c+32\), which is not equivalent to \(4c + 8\).

Step4: Analyze Option C

Option C is \(4(4c + 2)\). Using the distributive property, \(4(4c + 2)=16c+8\), which is not equivalent to \(4c + 8\).

Step5: Analyze Option D

Option D is \(4(c + 2)\), which is the factored form we found in Step 1, so it is equivalent to the original expression.

Answer:

A. \((c + 2)4\), D. \(4(c + 2)\)