Question 190657
{{{-9r^2+1}}} Start with the given expression.



{{{1-9r^2}}} Rearrange the terms



{{{(1)^2-9r^2}}} Rewrite {{{1}}} as {{{(1)^2}}}.



{{{(1)^2-(3r)^2}}} Rewrite {{{9r^2}}} as {{{(3r)^2}}}.



Notice how we have a difference of squares {{{A^2-B^2}}} where in this case {{{A=1}}} and {{{B=3r}}}.



So let's use the difference of squares formula {{{A^2-B^2=(A+B)(A-B)}}} to factor the expression:



{{{A^2-B^2=(A+B)(A-B)}}} Start with the difference of squares formula.



{{{(1)^2-(3r)^2=(1+3r)(1-3r)}}} Plug in {{{A=1}}} and {{{B=3r}}}.



So this shows us that {{{-9r^2+1}}} factors to {{{(1+3r)(1-3r)}}}.



In other words {{{-9r^2+1=(1+3r)(1-3r)}}}.