 # Playing with Numbers.. A few different ways of looking at the same thing

\begin{align} \text{Base 70}\\ x & = 69*79\\ & = 69^\underline {-1}*79^\underline{ +9}\\ & = (79-1)*(7*10)-9\\ & = 78 * 70 - 9\\ & = 5451\\ \\ \text{Base 80}\\ x & = 69*79\\ & = 69^\underline {-11}*79^\underline{ -1}\\ & = (69-1)*(8*10)+11\\ & = 68 * 80 + 11\\ & = 5451\\ \\ \text{Base 100}\\ x & = 69 * 79\\ & = 69^\underline {-31}*79^\underline{ -21}\\ & = (69-21)*100+(-31*-21)\\ & = 4800 + 651 \\ & = 5451\\ \\ \\ \text{Mixed Base 70 & 80}\\ x & = 69 * 79\\ & = (70-1) * ( 80-1)\\ & = 5600 - 70 - 80 + 1\\ & = 5600 - 150 +1\\ & = 5451\\ \\ \\ \text{Difference of Squares}\\ x & = 69 * 79\\ & = (69 + (79-69)/2)^2 - (79-69)/2\\ & = 74^2 -5^2 \\ & = 5451 \\ \\ \text{Criss Cross}\\ x & = 69 * 79\\ & = (60*70) + (60*9) + (70*6)+ (9*9)\\ & = 4200 + (540 + 420) + 81\\ & = 5451\\ \\ \text{When I have brain freeze}\\ x & = 69 * 79\\ & = (69*70) + (69*9) \\ \text( OR )\\ &=(69*70)+540+81\\ & = 5451\\ \\ \\ \text{Ending in the same number (9)}\\ x & = 69 * 79\\ & = 4200 + 69*9 + 70*9\\ & = 4200 + 139*9\\ \text{!!139*9}\\ & = 4200 + ( 139 * 10 ) - 39\\ & = 4200 + 1390 - 9\\ & = 5451\\ \\ \end{align}
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I see what you are doing and love it.
I know you said ‘please ignore’, but I could not.