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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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(5x-2)(5x-2) x=2/5
sorry,not x but s
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.

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hold the phone. it says "factor" not solve for x. you do not have an equation here so do not write x = anything!
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
the value of s just an extra...
it would help to write as \[25s^2-20s+4\] and recognize this as a "perfect square"
\[25s^2\] is the square of \[5s\] 4 is the square of -2 and \[-20x =2\times -2\times 5x\]
so right away you get \[(5x-2)^2\] because \[(a-b)^2=a^2-2ab+b^2\]
There is a nice illustration of that here: http://en.wikipedia.org/wiki/File:A_plus_b_au_carre.svg
Oh for goodness sake... http://upload.wikimedia.org/wikipedia/commons/c/c2/A_plus_b_au_carre.svg

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