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To solve a multiplication problem in two different ways, you can first use the standard algorithm, where you multiply the numbers directly and manage carries as needed. Alternatively, you can apply the distributive property, breaking one of the numbers into smaller, more manageable parts, multiplying each part separately, and then summing the results. For example, for 12 x 15, you could compute it as (10 + 2) x 15 and then calculate 10 x 15 + 2 x 15. Both methods will yield the same answer.

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