Factor this unless it is fully factored?

Question

#18rs^2 - 2r#

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Answer 1 · 2018-04-30T06:10:36

#2r(9s^2-1)#

#18rs^2-2r=2r(9s^2-1)#

Answer 2 · 2018-04-30T06:11:21

#18rs^2-2r = 2r(3s-1)(3s+1)#

Given:

#18rs^2-2r#

Note that both terms are divisible by #2r#, so we can separate that out as a factor...

#18rs^2-2r = 2r(9s^2-1)#

Note that both #9s^2 = (3s)^2# and #1 = 1^2# are perfect squares.

So we can use the difference of squares identity:

#A^2-B^2=(A-B)(A+B)#

with #A=3s# and #B=1# to find:

#9s^2-1 = (3s)^2-1^2 = (3s-1)(3s+1)#

Putting it all together:

#18rs^2-2r = 2r(3s-1)(3s+1)#