How do you multiply #(2a ^ { 3} - a + 3) ( a ^ { 2} + 3a - 5)#?

1 Answer
EZ as pi
Nov 6, 2016

#=2a^5 +6a^4-11a^3+14a-15#

Explanation:

Each of the terms in the first bracket (factor) must be multiplied by each of the terms in the second bracket (factor).
You will end up with 9 terms to begin with, then you will be able to add the like terms together.

#(color(blue)(2a^3)color(magenta)( - a)color(lime)( + 3))(a^2 + 3a - 5)#

#=color(blue)(2a^3)(a^2 + 3a - 5) color(magenta)( - a) (a^2 + 3a - 5) color(lime)( + 3)(a^2 + 3a - 5)#

#=color(blue)(2a^5 +6a^4-10a^3)color(magenta)(-a^3-3a^2+5a)color(lime)(+3a^2+9a-15#

#=2a^5 +6a^4-10a^3-a^3-cancel(3a^2)+5acancel(+3a^2)+9a-15#

#=2a^5 +6a^4-11a^3+14a-15#

It is good practice to answer in descending powers of #a#

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