# How do you factor #2p^3-162p#?

##### 1 Answer

#### Explanation:

The first step is to take out the

#color(blue)"common factor"# of 2p

#rArr2p(p^2-81)tocolor(red)((1)#

#" the factor " (p^2-81)" is a " color(blue)"difference of squares"#

#"and factorises, in general as"#

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

#"here " a=p" and " b=9#

#rArrp^2-81=(p-9)(p+9)#

#"returning to " color(red)((1))#

#rArr2p^3-162p=2p(p-9)(p+9)#