Algebra I in Simple English/Factoring/Factoring a^2-b^2 Binomials - Free test prep materials from TestsAndTutors.com

Algebra I in Simple English/Factoring/Factoring a^2-b^2 Binomials

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Difference of Squares

Any binomial of the form $a 2 - b 2$ may be written as $(a+b) \cdot (a-b)$ . That is

$a^2 - b^2 = (a-b) \cdot (a+b)$ .

Example 1: Factor $x 2 - 9$ .

This is clearly seen just take $a 2 = x 2$ and $b 2 = 9$ so that $b = 3$ . So $x 2 - 9 = (x - 3)(x + 3)$

Example 2:: $32 w 4 - 162$ .

Here is is unclear where we can use the difference of squares as 32 is NOT a perfect square. However if we look we see that we can factor out a common factor of 2.

$32 w 4 - 162 = 2(16 w 4 - 81)$

Now we see we can use the difference of two squares to simplify matters take $a 2 = 16 w 4$ and $b 2 = 81$ :

$2(16 w 4 - 81) = 2(4 w 2 - 9)(4 w 2 + 9)$

Now we notice that we can use the difference of squares again in the first factor to get:

$2(4 w 2 - 9)(4 w 2 + 9) = 2(2 w + 3)(2 w - 3)(4 w 2 + 9)$

This is now completely factored.

This is brings us to our next point that is that $a 2 + b 2$ is NOT FACTORABLE (at least for the purposes of this class).

Extracted from http://en.wikibooks.org/wiki/Algebra_I_in_Simple_English. Reproduced under the GNU Free Documentation License

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