How do you factor #125u^2-50u+5#?

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Answer 1 · 2016-08-12T12:12:23

Factor by breaking into pieces by first taking out the 5 to give
#5(25x^2-10x + 1)# which factors to
= #5 (5x -1) ( 5x -1)#
=# 5( 5x -1)^2#

There is a common factor of 5 in all three terms. Dividing out the common factor simplifies the expression so

#125 x^2 - 50 x + 5# = #5(25x^2 -10x + 1)#

This is a perfect square trinomial.

25 can be factored into 5 x 5 and 1 can be factored into 1 x1

The trinomial factor can now be factored into two binomials

#5(25x^2 -10 x + 1)#

=#5( 5x -1)( 5x -1)#

=#5( 5x -1)^2#