hich expression is equivalent to 54n-20m+6n?
A. 40mn
B. 60n+20m
C. 20(m-3n)
D. 20(3n-m)
B. 60n+20m
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To find the expression that is equivalent to 54n - 20m + 6n, we can simplify the expression by combining like terms. Like terms refer to terms that have the same variables raised to the same powers.
In the given expression, we have two terms with the variable 'n' and one term with the variable 'm':
54n - 20m + 6n
Combining the 'n' terms, we add the coefficients (numbers in front of the variables) together:
54n + 6n = 60n
Our expression now becomes:
60n - 20m
Therefore, the equivalent expression is 60n - 20m.
Among the answer choices:
A. 40mn - This expression has the product of 'n' and 'm', which is not present in the original expression.
B. 60n + 20m - This expression has the sum of 'n' and 'm', which is not present in the original expression.
C. 20(m-3n) - This expression has the difference of 'm' and '3n', which is not present in the original expression.
D. 20(3n-m) - This expression has the difference of '3n' and 'm', which matches the simplified form of the original expression, 60n - 20m.
Therefore, the correct answer is D. 20(3n-m).