How do you evaluate #(a + 9) ^ { 2} - ( a - 4) ^ { 2}#?

2 Answers
Martin C.
Jan 30, 2018

#26a+65#

Explanation:

#(a+9)^2-(a-4)^2#
#=a^2+18a+9^2-a^2+8a-4^2#
#=18a+8a+81-16#
#=26a+65#

Jim G.
Jan 30, 2018

#26a+65#

Explanation:

#"this is a "color(blue)"difference of squares"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#(a+9)^2-(a-4)^2#

#"with "a=a+9" and "b=a-4#

#=(a+9-(a-4))(a+9+a-4)#

#=(cancel(a)+9cancel(-a)+4)(2a+5)#

#=13(2a+5)#

#=26a+65#

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