How do you factor #3r^3-192r#?

1 Answer
Jan 4, 2017

Answer:

#3r(r-8)(r+8)#

Explanation:

The first step is to take out a #color(blue)"common factor"# of 3r

#rArr3r(r^2-64)#

We now have a #color(blue)"difference of squares"# inside the bracket, which 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 = r" and " b=8#

#rArrr^2-64=(r-8)(r+8)#

#"Pulling it all together gives"#

#3r^3-192r=3r(r-8)(r+8)#