Question

write an equivalent expression.
4d + 24
select all that apply.
a. 4(d + 8)
b. 4(d + 24)
c. (d + 6)4
d. 4(4d + 6)

Explanation:

Step1: Factor out 4 from \(4d + 24\)

We use the distributive property \(ab+ac = a(b + c)\). Here, \(a = 4\), \(b = d\), and \(c = 6\) (since \(4\times6=24\)). So \(4d+24=4(d + 6)\).

Step2: Analyze option A

Option A is \(4(d + 6)\), which matches the factored form we found.

Step3: Analyze option B

Option B is \(4(d + 24)\). Expanding this gives \(4d+96\), which is not equal to \(4d + 24\), so B is incorrect.

Step4: Analyze option C

Multiplication is commutative, so \((d + 6)4=4(d + 6)\) (by the commutative property of multiplication \(ab=ba\)). So this is equivalent to \(4d + 24\).

Step5: Analyze option D

Expanding option D: \(4(4d+6)=16d + 24\), which is not equal to \(4d + 24\), so D is incorrect.

Answer:

A. \(4(d + 6)\), C. \((d + 6)4\)