How do you combine like terms in #(2a + 3) ^ { 2} + ( a - 5) ^ { 2}#?

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Answer 1 · 2018-06-09T18:42:42

#5a^2+2a+34#

Using the formulas

#(a+b)^2=a^2+2ab+b^2#
#(a-b)^2=a^2-2ab+b^2#
we get

#4a^2+9+12a+a^2-10a+25#
and this is

#5a^2+2a+39#

Answer 2 · 2018-06-09T18:43:18

#5a^2+2a+34#

First FOIL the squared terms:

#=(2a+3)^2+(a-5)^2#

#=(2a+3)(2a+3)+(a-5)(a-5)#

#=4a^2+6a+6a+9+a^2-5a-5a+25#

now "combine like terms":

#=5a^2+2a+34#