Question 143186
Do you want to factor this?


Let {{{y=x-5}}}



So {{{100-(x-5)^2}}} becomes {{{100-y^2}}}. Notice how we have a difference of squares




{{{(10+y)(10-y)}}} Factor the expression using the difference of squares formula {{{A^2-B^2=(A+B)(A-B)}}}



{{{(10+x-5)(10-(x-5))}}} Plug in {{{y=x-5}}}



{{{(10+x-5)(10-x+5)}}} Distribute



{{{(5+x)(15-x)}}} Combine like terms



So {{{100-(x-5)^2}}} factors to {{{(5+x)(15-x)}}}