factor completely:
25s^2+4-20s

Question

mohsen · Answer

(5x-2)(5x-2)

x=2/5

mohsen · Answer

sorry,not x but s

mathteacher1729 · Answer

As a general technique for solving these problems, we know we want our answer to look like ( stuff ) * (stuff) , to be more specific, we want it to look like ( number* s plus/minus number) * ( number*s plus/minus number). 

In this case you can see that the 25 multiplied by s^2 can factor only into 5*5 or 1*25.  (that's where the 5x comes from).  From there it's filling in the steps of FOIL.

anonymous · Answer

hold the phone.  it says "factor" not solve for x.  you do not have an equation here so do not write x = anything!

mathteacher1729 · Answer

I would recommend checking out these videos: http://www.mathtv.com go to algebra > quadratic equation > factoring polynomials, and watch all the ones with the old guy. He is awesome. :D

mohsen · Answer

the value of s just an extra...

anonymous · Answer

it would help to write as 
$$25s^2-20s+4$$ and recognize this as a "perfect square"

anonymous · Answer

$$25s^2$$ is the square of $$5s$$
4 is the square of -2
 and $$-20x =2\times -2\times 5x$$

anonymous · Answer

so right away you get 
$$(5x-2)^2$$ because 
$$(a-b)^2=a^2-2ab+b^2$$

mathteacher1729 · Answer

There is a nice illustration of that here: http://en.wikipedia.org/wiki/File:A_plus_b_au_carre.svg

mathteacher1729 · Answer

Oh for goodness sake... http://upload.wikimedia.org/wikipedia/commons/c/c2/A_plus_b_au_carre.svg