Question

write an equivalent expression.
3(d - 4)

select all that apply.
a. 3d - 12
b. 3d - 4
c. 4(d - 3)
d. (d - 4)3

Explanation:

Step1: Apply Distributive Property

The distributive property states that \(a(b - c)=ab - ac\). For \(3(d - 4)\), we distribute the 3: \(3\times d-3\times4 = 3d - 12\). So option A is equivalent.

Step2: Check Commutative Property of Multiplication

The commutative property of multiplication says \(ab = ba\). So \(3(d - 4)=(d - 4)3\). Thus, option D is equivalent.

Step3: Analyze Other Options

• For option B: \(3d-4\) is not equal to \(3d - 12\), so it's not equivalent.
• For option C: Distribute \(4(d - 3)=4d-12\), which is not equal to \(3d - 12\) or \(3(d - 4)\), so it's not equivalent.

Answer:

A. \(3d - 12\), D. \((d - 4)3\)