+0  
 
0
200
2
avatar+558 

Factor

 Jan 27, 2018
 #2
avatar+2324 
+1

\(49x^8-16y^{14}\) can be written as a difference of squares.

 

\(49x^8-16y^{14}\Rightarrow\left(\textcolor{red}{7x^4}\right)^2-\left(\textcolor{blue}{4y^7}\right)^2\) This proves that this expression can be written as a difference of squares. Remember that a difference of squares can be factored using the following rule: \(\textcolor{red}{a}^2-\textcolor{blue}{b}^2=(\textcolor{red}{a}+\textcolor{blue}{b})(\textcolor{red}{a}-\textcolor{blue}{b})\)
\(\hspace{5mm}\textcolor{red}{a}^2\hspace{3mm}-\hspace{5mm}\textcolor{blue}{b}^2\hspace{4mm}=(\hspace{2mm}\textcolor{red}{a}\hspace{2mm}+\hspace{3mm}\textcolor{blue}{b})(\hspace{2mm}\textcolor{red}{a}\hspace{4mm}-\hspace{2mm}\textcolor{blue}{b})\\ \left(\textcolor{red}{7x^4}\right)^2-\left(\textcolor{blue}{4y^7}\right)^2=(\textcolor{red}{7x^4}+\textcolor{blue}{4y^7})(\textcolor{red}{7x^4}-\textcolor{blue}{4y^7})\) Notice how the rule and this particular expression go hand in hand. I introduced colors to ease understanding. At this point, no more can be done. 
   
 Jan 27, 2018

20 Online Users

avatar
avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.