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
A and D are equivalent to 6m + 18.
To determine which expressions are equivalent to 6m + 18, we can simplify each option by applying the distributive property and combining like terms.
A) 6(m + 18) = 6m + 108
B) 6(m + 3) = 6m + 18
C) 6 + m + 18 = 24 + m
D) 2(3m + 9) = 6m + 18
E) 5m + 10 + 8 + m = 6m + 18
From the simplification, we can see that options B, D, and E are equivalent expressions to 6m + 18.
So, the expressions that are equivalent to 6m + 18 are:
B) 6(m + 3)
D) 2(3m + 9)
E) 5m + 10 + 8 + m
To find the expressions that are equivalent to 6m + 18, we need to simplify and factor out common terms. Let's analyze each option.
A) 6(m + 18)
This expression is equivalent to 6 times the sum of m and 18. Distributing the 6 yields 6m + 108. Since this does not match the original expression, it is not equivalent.
B) 6(m + 3)
This expression is equivalent to 6 times the sum of m and 3. Distributing the 6 yields 6m + 18. This matches the original expression, so it is equivalent.
C) 6 + m + 18
This expression involves adding 6, m, and 18. Simplifying gives 24 + m, which does not match the original expression. Thus, it is not equivalent.
D) 2(3m + 9)
This expression is equivalent to 2 times the sum of 3m and 9. Distributing the 2 gives 6m + 18. This matches the original expression, so it is equivalent.
E) 5m + 10 + 8 + m
In this expression, we have terms 5m, 10, 8, and m. Simplifying gives 6m + 18, which matches the original expression and is thus equivalent.
Based on the analysis, the expressions that are equivalent to 6m + 18 are:
B) 6(m + 3)
D) 2(3m + 9)
E) 5m + 10 + 8 + m