Expert: Abe Mantell - 7/27/2011

Question
Could you please explain how to determine if a polynomial is the difference between two squares?  I am taking online school and am horrible at algebra, I just have a hard time understanding it.  Thanks so much for any help!!

Answer
Hello Jenn,

The difference of two squares is of the form: x^2 - y^2, which factors to (x-y)(x+y)

For example:
1. 4a^2-b^2 = (2a)^2 - b^2 = (2a-b)(2a+b)

2. 9x^6-16y^4 = (3x^3)^2 - (4y^2)^2 = (3x^3-4y^2)(3x^3+4y^2)

See?  For more check these sites:
http://regentsprep.org/REgents/math/ALGEBRA/AV6/Lfactps.htm
http://www.algebrahelp.com/lessons/factoring/differencebetweensquares/
http://www.barstow.edu/lrc/tutorserv/handouts/079%20Factoring%20A%20Difference%2...
http://dcsd.k12.nv.us/other/pdc/mathbuilder/mathdict/word/proce/exp_85/ref-1-id-...

I hope this helps.

Abe