Hello I have a new question!

The question is (originally written in swedish):

Divide Factors: 64x^4-4x^2

My answer: 4x^2(16x^2-1)

Mozziee
Jul 27, 2014

#2**+10 **

Thanks Alan, I just explain a little further,

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

so

\boxed{a^2-b^2=(a-b)(a+b)}\\\\

\mbox{This is referred to as a difference of two squares and you need to memorize it.}\\\\

\begin{array}{rll}

16x^2-1&=&(4x)^2-1^2\\\\

&=&(4x-1)(4x+1)

\end{array}$$

Melody
Jul 27, 2014

#1**+10 **

Yes, though you can take it a little further to get: 4x^2(4x+1)(4x-1)

So the factors are: 4, x^2, 4x+1 and 4x-1 (and various combinations of these).

Alan
Jul 27, 2014

#2**+10 **

Best Answer

Thanks Alan, I just explain a little further,

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

so

\boxed{a^2-b^2=(a-b)(a+b)}\\\\

\mbox{This is referred to as a difference of two squares and you need to memorize it.}\\\\

\begin{array}{rll}

16x^2-1&=&(4x)^2-1^2\\\\

&=&(4x-1)(4x+1)

\end{array}$$

Melody
Jul 27, 2014