# How do you factor #9x^3-x#?

##### 3 Answers

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There is a

#color(blue)"common factor"# of x in both terms.

#rArrx(9x^2-1)larrcolor(red)"remove common factor"#

#9x^2-1" is a"color(blue)" difference of squares"# and factorises, in general as shown.

#color(red)(bar(ul(|color(white)(2/2)color(black)(a^2-b^2=(a-b)(a+b))color(white)(2/2)|)))#

#"here " (3x)^2=9x^2" and " 1^2=1#

#rArra=3x" and " b=1#

#rArr9x^2-1=(3x-1)(3x+1)#

#rArr9x^3-1=x(3x-1)(3x+1)larrcolor(red)" fully factorised"#