How do you factor #c² - 12cd - 85d²#?

2 Answers
Jim G.
Mar 3, 2018

#(c-17d)(c+5d)#

Explanation:

#"using the a-c method"#

#"the factors of - 85 which sum to - 12 are - 17 and + 5"#

#rArrc^2-12cd-85d^2=(c-17d)(c+5d)#

MattyMatty
Mar 3, 2018

#(c + 5d)(c - 17d)#

Explanation:

#c^2 - 12 cd - 85 d^2 = (c + ad)(c - bd)#

#=> ab = 85, a-b = -12#

#=> a = b - 12#
#=> (b-12)b = 85#
#=> b^2 - 12 b - 85 = 0#
#"disc = "12^2 + 4*85 = 484 = 22^2#
#=> b = (12 pm 22)/2 = 6 pm 11 = -5 or 17#
#=> (a,b) = (-17,-5) or (5,17)#

#=> c^2 - 12 cd - 85 d^2 = (c + 5d)(c - 17d)#

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