Question

3 which expressions are equivalent to 6m + 18? select all that apply. a 6(m + 18) b 6(m + 3) c 6 + m + 18 d 2(3m + 9) e 5m + 10 + 8 + m

Explanation:

Step1: Analyze Option A

Expand \(6(m + 18)\) using the distributive property: \(6\times m+6\times18 = 6m + 108\), which is not equal to \(6m + 18\). So A is incorrect.

Step2: Analyze Option B

Expand \(6(m + 3)\) using the distributive property: \(6\times m+6\times3=6m + 18\), which matches the given expression. So B is correct.

Step3: Analyze Option C

Simplify \(6 + m + 18\) to \(m+24\), which is not equal to \(6m + 18\). So C is incorrect.

Step4: Analyze Option D

Expand \(2(3m + 9)\) using the distributive property: \(2\times3m+2\times9 = 6m+18\), which matches the given expression. So D is correct.

Step5: Analyze Option E

Combine like terms in \(5m + 10 + 8 + m\): \((5m + m)+(10 + 8)=6m + 18\), which matches the given expression. So E is correct.

Answer:

B. \(6(m + 3)\), D. \(2(3m + 9)\), E. \(5m + 10 + 8 + m\)