How do you factor completely: 2x^3 - 18x2x3−18x?

1 Answer
Alan P.
Jul 21, 2015

2x^3-18x = (2x)(x+3)(x-3)2x3−18x=(2x)(x+3)(x−3)

Explanation:

Given 2x^3-18x2x3−18x

Remove the obvious common factor (2x)(2x)
color(white)("XXXX")XXXX=(2x)(x^2-9)=(2x)(x2−9)

Recognize the second term as the difference of squares
color(white)("XXXX")XXXX=(2x)(x+3)(x-3)=(2x)(x+3)(x−3)
color(white)("XXXX")XXXXcolor(white)("XXXX")XXXXcolor(white)("XXXX")XXXXSince (x^2-a^2) = (x+a)(x-a)(x2−a2)=(x+a)(x−a)

Related questions
See all questions in Factoring Completely
Impact of this question
1464 views around the world
You can reuse this answer
Creative Commons License