Question

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?

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