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

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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!

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