To simplify the expression \( 10(2m + 6) \) using the distributive property, you will multiply 10 by each term inside the parentheses.
Here are the steps:
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Distribute \( 10 \) to \( 2m \): \[ 10 \times 2m = 20m \]
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Distribute \( 10 \) to \( 6 \): \[ 10 \times 6 = 60 \]
Now, combine the results from both distributions:
\[ 10(2m + 6) = 20m + 60 \]
So, the simplified expression is:
\[ \boxed{20m + 60} \]