Question #d8676

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Answer 1 · 2018-01-07T01:39:01

#(9)(47)(49)#

.

#144^2-9=144^2-3^2#

Using:

#a^2-b^2=(a-b)(a+b)#

#144^2-3^2=(144-3)(144+3)=(141)(147)=(3)(47)(3)(49)=(9)(47)(49)#

Answer 2 · 2018-01-07T02:08:10

#(144 + 3) (144 - 3)#
#color(white)(....)# #(147)# #(141)#

The expression #144^2 - 9# is a Difference of Two Squares.
It's the same as #144^2 - 3^2#

The factorization of the Difference of Two Squares (by memory):

#color(white)(.....)##a^2 - b^2#

#(a + b)(a - b)#

#color(white)(............)#— — — — — — — — — —

Factor

#color(white)(.)#.#a^2 - b^2#
#144^2 - 3^2#

#( a + b)( a - b)#
#(144 + 3)(144 - 3)# #larr# answer

#color(white)(............)#— — — — — — — — — —

I wonder if this question was written to be a challenge.
Maybe the textbook is trying to see if you get confused?

Possibly a student might mix up these two problems:

A student who is accidentally solving this:
#color(white)(..)##144^("forgetting the" ^(2)# - #9#
#color(white)(..)##144# - #9#

will get this incorrect answer:
#(12 + 3) ( 12 - 3)#
#(15)(9)#