when multiplying a sum of two numbers by a third number, we can add the two numbers and then multiply by the third number, or we can multiply each number of the dumb by the third number and then add the two products

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Yes, you are correct. The order of operations doesn't affect the result when multiplying a sum of two numbers by a third number. You can either add the two numbers first and then multiply by the third number or multiply each number by the third number separately and then add the two products. The distributive property of multiplication over addition guarantees that both methods will give the same result.
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