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SFFT (Simon's Favorite Factoring Trick)
Toolkit 23
SFFT (Simon's Favorite Factoring Trick)
x
y
+
a
x
+
b
y
=
c
⇒
(
x
+
b
)
(
y
+
a
)
=
c
+
a
b
xy+ax+by=c\;\Rightarrow\;(x+b)(y+a)=c+ab
x
y
+
a
x
+
b
y
=
c
⇒
(
x
+
b
)
(
y
+
a
)
=
c
+
ab
GSFFT (General Form)
\text{GSFFT (General Form)}
GSFFT (General Form)
a
x
y
+
b
x
+
c
y
=
d
axy+bx+cy=d
a
x
y
+
b
x
+
cy
=
d
a
2
x
y
+
a
b
x
+
a
c
y
=
a
d
a^2xy+abx+acy=ad
a
2
x
y
+
ab
x
+
a
cy
=
a
d
(
a
x
+
c
)
(
a
y
+
b
)
=
a
d
+
b
c
(ax+c)(ay+b)=ad+bc
(
a
x
+
c
)
(
a
y
+
b
)
=
a
d
+
b
c
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