Factor 15r2 plus 2rs-s2

Answer 1

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)