When adding two numbers, such as 123 and 423, care is taken to first line them up and then add like digits. How does expanding this expression to [ (1 * 10^2) + (2 * 10^1) + (3 * 10^0) ] + [ (4 * 10^2) + (2 * 10^1) + (3 * 10^0) ] make the operation more like a polynomial addition problem?

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Mathematics

America Petersen

3 November, 09:15

When adding two numbers, such as 123 and 423, care is taken to first line them up and then add like digits. How does expanding this expression to [ (1 * 10^2) + (2 * 10^1) + (3 * 10^0) ] + [ (4 * 10^2) + (2 * 10^1) + (3 * 10^0) ] make the operation more like a polynomial addition problem?

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Casey · Answer 1

Since a polynomial is where we have like terms such as (1 x 10²) and (4 x 10²), we can add these up using the distributive property to get (5 x 10²) but still keep the 10². For example, it's similar to if we had 2x²+3x²=5x². The x² is still there, but we add up the 2 and 3. Similarly, we can add these up for 10^1 and 10^0