# Thread: Ti-83 difference of squares

1. ## 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?

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

3. Sorry that was a typo, and my question is where does the come from, and from what operation exactly in the calculator?

4. Hello Allyourbass,

What squared is 16? Simply input $\displaystyle \frac{1}{16}^{\frac{1}{2}}$ into your calculator and it will yield$\displaystyle \frac{1}{4}$

5. Originally Posted by allyourbass2212
Sorry that was a typo, and my question is where does the 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.

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