How do you factor the trinomial #a^2 - 4ab + 4b^2#?

Question

5867 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-19T15:11:19

#(a-2b)(a-2b)#

#=a^2-2ab-2ab+4b^2#
#=a(a-2b)-2b(a-2b)#
#=(a-2b)(a-2b)#

Answer 2 · 2016-03-19T16:09:23

Have a look at how I build it up

#a^2" has to be from "axxa#

So we start with: #(a+?)(a+?)#

Notice that #2xx2=4" and that "2+2=4#

But in the question we have #-4ab#. So we can not have 2+2 but instead we must have #-2-2=-4#

So our next step is

#(a-2?)(a-2?)#

But we have #b^2# so we need #bxxb#

So we must have:

#(a-2b)(a-2b)" "=" "a^2-2ab-2ab+4b^2" "# It works!