How do you factor #16x^2 -40x +25#?

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Answer 1 · 2016-05-22T16:07:20

#(4x-5)( 4x-5)=(4x-5)^2#

This is a pretty straight forward question.

We know that #color(red)((a-b)^2=a^2-2ab+b^2)#

Compare #a^2-2ab+b^2# to # 16x^2-40x+25#

Lets look at #a^2# and #b^2#

#a^2=16x^2# and #b^2=25#

#=>a=4x# and #b=5#

Then, #2ab=2xx4x xx5 = 40x#, as given in the expression.

Therefore,

#16x^2-40x+25#

#=(4x)^2 - (2 xx 4x xx5) + 5^2#

#=(4x-5)^2#

The factors are #4x-5, 4x-5#