How do you factor the trinomial #3(a + b)^2 - 18(a + b) - 216#?

1 Answer
Jim G.
Mar 30, 2018

#3(a+b-12)(a+b+6)#

Explanation:

#"using the substitution "x=a+b#

#rArr3(a+b)^2-18(a+b)-216#

#=3x^2-18x-216#

#"take out a "color(blue)"common factor "3#

#=3(x^2-6x-72)#

#"the factors of - 72 which sum to - 6 are - 12 and + 6"#

#=3(x-12)(x+6)#

#"change x back to "a+b#

#=3(a+b-12)(a+b+6)#

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