# decompose some polynomials

[ In first, I say "I'm sorry!", because I am not a Englishman and I don't know your language terms very well. ]

OK, I have some polynomials (like $a^2 +2ab +b^2$ ). And I can't decompress these (for example $a^2 +2ab +b^2 = (a+b)^2$).

Can you help me? (if you can, please write the name or formula of combination (like $(a+b)^2 = a^2 +2ab +b^2$) of each polynomial.

1. $(a^2-b^2)x^2+2(ad-bc)x+d^2-c^2$

2. $2x^2+y^+2x-2xy-2y+1$

3. $2x^2-5xy+2y^2-x-y-1$

4. $x^6-14x^4+49x^2-36$

5. $(a+b)^4+(a-b)^4+(a^2-b^2)^2$

Thank you! very much ....

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Where are you stuck? –  Aryabhata Jan 22 '11 at 18:08
The English term for what you want to do (which you called "decompress") is "factor a polynomial". There also appears to be a typo in your second polynomial (it contains the expression $y^+$). –  Willie Wong Jan 22 '11 at 18:24

For

1) $(a^2-b^2)x^2+2(ad-bc)x+d^2-c^2$

$$(a^2-b^2)x^2+2(ad-bc)x+d^2-c^2=a^2x^2+2adx+d^2-(b^2x^2+2bcx+c^2)$$

The same idea can be applied to all your questions.

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Thank you .... you say correct .. –  jiun Jan 22 '11 at 19:00

Looks like most of these can be done through factoring by "grouping". There are some ways and more practice problems here: http://cnx.org/content/m21901/latest/

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