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How do you factor by grouping # b^2 - 8b + 16 - c^2 #?

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May 17, 2015

#b^2-8b+16-c^2#
#= (b^2-8b+16)-c^2#
#= (b-4)^2 - c^2#
#= ((b-4)+c)((b-4)-c)#
#= (b+c-4)(b-c-4)#

The factoring of #(b-4)^2 - c^2# as #((b-4)+c)((b-4)-c)# is an instance of the identity:

#m^2-n^2=(m+n)(m-n)#

with #m=b-4# and #n=c#.

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