Can Someone walk through how Capitalized Software Expenses flow through 3 statements?

Have not dealt with software companies often so curious to hear how capitalized software expenses would flow through the three financial statements. My thinking below for $100M of capitalized software expense assuming amortization of 10 years but please correct me if incorrect!

Time 0:

IS: no impact to income statement as the software expense is capitalized

CF: although the software expense is capitalized, would still recognize the actual cash outflow impact (would this be under CF from investing activities?) so cash down $100M

BS: Cash down $100M, capitalized software expense up $100M? I am not entirely sure here as 10Ks I have seen treat capitalized software like intangible assets so do you need to take into account DTLs?

Time 1:

IS: You have $10M of amortization expenses associated with the capitalized software expense, assuming 30% tax rate, $7M decrease in net income

CF: Net income down $7M but amortization expense of capitalized software not actual cash outflow so add back $10M. Positive net change in CF of $3M

BS: Cash up $3M, capitalized software balance down $10M, overall asset side down $7M. Decrease in net income of -$7M flows into shareholder equity so BS balances