+0  
 
0
87
2
avatar+468 

Factor

SamJones  Jan 27, 2018
Sort: 

1+0 Answers

 #2
avatar+1870 
+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. 
   
TheXSquaredFactor  Jan 27, 2018

18 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details