Question

select the expressions that are equivalent to 6(q + 3). (3 + q)6 6q + 18 9q (q + 3)6

Explanation:

Step1: Analyze \((3 + q)6\)

Multiplication is commutative, so \(a\times b = b\times a\). Here, \(6(q + 3)=(q + 3)6=(3 + q)6\) (since addition is commutative, \(q + 3=3 + q\)). So \((3 + q)6\) is equivalent.

Step2: Analyze \(6q + 18\)

Using the distributive property \(a(b + c)=ab+ac\), for \(6(q + 3)\), we have \(6\times q+6\times3 = 6q+18\). So \(6q + 18\) is equivalent.

Step3: Analyze \(9q\)

\(6(q + 3)=6q + 18\), and \(6q+18
eq9q\) (unless \(q = 6\), but we need equivalent for all \(q\)). So \(9q\) is not equivalent.

Step4: Analyze \((q + 3)6\)

Multiplication is commutative, so \(6(q + 3)=(q + 3)6\). So \((q + 3)6\) is equivalent.

Answer:

A. \((3 + q)6\)
B. \(6q + 18\)
D. \((q + 3)6\)