#89^2 # is the same as #89xx89 = 7921# by calculator
There are various way of multiplying without a calculator & this is just 1 of them. It is splitting up the numbers. The mathematical name for this process of splitting up is partitioning.
Note this trick for multiplying #80xx80# in your head
80 is #8xx10# so #80xx80 -> 8xx10xx8xx10#
#" "->8xx8xx100#
#" "->64xx100#
#" "->6400#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(white)(.)6400#
#color(white)(..)720#
#color(white)(..)720#
#ul(color(white)(7..)81) larr" Add"#
#color(white)(.)7921#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("The traditional way looks like this")#
#color(white)(64)color(green)(89)#
#ul(color(white)(64)color(blue)(89)) larr" multiply"#
#7120 larr"this line is "color(green)(89)color(blue)(xx80)#
#ul(color(white)(6)801) larr "this line is "color(green)(89)color(blue)(xx9)#
#7921 larr"All added up"#
#color(brown)("So really the traditional way is still partitioning. It is just that it is")# #color(brown)("partitioned differently.
")#
