How do you multiply #(x ^ { 2} - 5x ) ( 5x - 25)#?

2 Answers
Camilleon
May 14, 2018

#5x^3# - #50x^2# + #125x#

Explanation:

F.O.I.L.

First, Outer, Inner, Last: order of terms to multiplied

First terms:
(x^2 - 5x)(5x - 25)

#5x# * #x^2# = #5x^3#

Outer terms:
(x^2 - 5x)(5x - 25)

#x^2# * #-25# = #-25x^2#

Inner terms:
(#x^2# - 5x)(5x - 25)

#-5x * 5x# = #-25x^2#

Last terms:
(#x^2# - 5x)(5x - 25)

#-5x * -25# = #125x# because two negatives make a positive.

Add all your terms together:

#5x^3# - #25x^2# #-25x^2# + #125x#

Combine like terms.

#5x^3# - #50x^2# + #125x#

Eric S.
May 14, 2018

Through distribution

Explanation:

First take #x^2# * 5x, then #x^2# * -25, after distributing the #x^2# do the same with the -5x in the first parenthesis. After getting your solutions ( #5x^3#+ #25x^2#- # 10x^2+125x#) you can simplify. Adding the #25x^2# and the #10x^2# getting #35x^2#.

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