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15rr+2rs-ss
axx+bx+c
a=15
b=2
c=-1
Multiply a and c:
15*-1=-15
Find multiples of ac that add up to b (d,e [ie de=ac, d+e=b]):
15=3*5
-15=-3*5, -5*3
Rewrite axx+bx+c into axx+dx+ex+c:
15rr+2rs-ss
15rr-3rs+5rs-ss
Factor sets of terms (ie axx+dx, and ex+c):
15rr-3rs+5rs-ss
3r(5r-s)+s(5r+s)
Combine like terms:
3r(5r-s)+s(5r+s)
(5r-s)(3r+s)
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