How do you multiply #(a + 2)(a^2 - 5a +9)#?

1 Answer
George C.
Jul 16, 2015

You can use distributivity to find:

#(a+2)(a^2-5a+9) = a^3-3a^2-a+18#

Explanation:

#(a+2)(a^2-5a+9)#

#=a(a^2-5a+9)+2(a^2-5a+9)#

#=(a^3-5a^2+9a)+(2a^2-10a+18)#

#=a^3-5a^2+2a^2+9a-10a+18#

#=a^3+(-5+2)a^2+(9-10)a+18#

#=a^3-3a^2-a+18#

Alternatively, look at each power of #a# in descending order and collect the terms that multiply to contribute to the coefficient of that power of #a#:

#a^3# : #a*a^2 = a^3#

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

#a# : #(a*9) + (2*-5a) = 9a-10a = -a#

#1# : #2 * 9 = 18#

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