# Ti-83 difference of squares

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• Aug 4th 2009, 08:20 AM
allyourbass2212
Ti-83 difference of squares
$\displaystyle x^n-c^n=(x^\frac{n}{2}-c\frac{n}{2})$

I like to use the calculator to double check myself, but for some reason I cannot produce the correct answer for the problem below.

$\displaystyle x^8-\frac{1}{16}=(x^4+\frac{1}{4})(x^4+\frac{1}{4})$
$\displaystyle =(x^2-\frac{1}{2})(x^2+\frac{1}{2})(x^4+\frac{1}{4})$

The first step I attempt to get $\displaystyle (x^4+\frac{1}{4})(x^4+\frac{1}{4})$ by putting this into the calculator$\displaystyle (\frac{1}{16})^{(\frac{1}{4})}$ which results in .5 or 1/2. How do I keep on missing the first step to the solution which is the 1/4?
• Aug 4th 2009, 02:16 PM
pickslides
Quote:

Originally Posted by allyourbass2212

$\displaystyle x^8-\frac{1}{16}=(x^4+\frac{1}{4})(x^4+\frac{1}{4})$

I don't think this is correct. I believe it is $\displaystyle x^8-\frac{1}{16}=(x^4-\frac{1}{4})(x^4+\frac{1}{4})$
• Aug 4th 2009, 08:22 PM
allyourbass2212
Sorry that was a typo, and my question is where does the http://www.mathhelpforum.com/math-he...645a4bee-1.gif come from, and from what operation exactly in the calculator?
• Aug 4th 2009, 08:40 PM
cmf0106
Hello Allyourbass,

http://www.mathhelpforum.com/math-he...ad330e17-1.gif

What squared is 16? Simply input $\displaystyle \frac{1}{16}^{\frac{1}{2}}$ into your calculator and it will yield$\displaystyle \frac{1}{4}$
• Aug 4th 2009, 09:52 PM
pickslides
Quote:

Originally Posted by allyourbass2212
Sorry that was a typo, and my question is where does the http://www.mathhelpforum.com/math-he...645a4bee-1.gif come from, and from what operation exactly in the calculator?

this comes from the difference of 2 squares rule.

$\displaystyle a^2-b^2 = (a-b)(a+b)$

$\displaystyle x^8-\frac{1}{16}$

$\displaystyle =(x^4)^2-\frac{1}{4^{-2}}$

$\displaystyle =(x^4)^2-(\frac{1}{4^{-1}})^2$

then applying the rule.

$\displaystyle =(x^4-\frac{1}{4})(x^4+\frac{1}{4})$