How do you factor the trinomial # (a + b)^2 - 9(a + b) - 36#?

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Answer 1 · 2015-11-29T02:45:34

#(a+b)^2-9(a+b)-36=(a+b+3)(a+b-12)#

#(a+b)^2-9(a+b)-36# is a quadratic equation in the form #ax^2+bx+c#, where #a=1, b=-9, and c=-36#.

For the time being, let #(a+b)=x#. After factoring with #x#, #(a+b)# will be substituted into the factors.

#x^2-9x-36#. Find two numbers that when added equal #-9# and when multiplied equal #-36#. The numbers #3# and #-12# meet the criteria.

Rewrite the expression.

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

Now substitute #(a+b)# back into the expression in place of #x#.

#(a+b)^2-9(a+b)-36=((a+b)+3)((a+b)-12)=(a+b+3)(a+b-12)#