Any Polynomial
Greatest Common Factor , commonly referred to as the GCF .
2
a
2
b
3
+
4
a
4
b
4
c
3
−
2
a
3
b
3
=
2
a
2
b
3
(
1
+
2
a
2
b
c
3
−
a
)
,
{\displaystyle 2a^{2}b^{3}+4a^{4}b^{4}c^{3}-2a^{3}b^{3}=2a^{2}b^{3}(1+2a^{2}bc^{3}-a),\,\!}
3
x
3
−
6
x
+
9
x
4
=
3
x
(
x
2
−
2
+
3
x
3
)
,
{\displaystyle 3x^{3}-6x+9x^{4}=3x(x^{2}-2+3x^{3}),\,\!}
4
x
(
x
+
2
)
+
3
x
2
(
x
+
2
)
=
(
x
+
2
)
(
4
x
+
3
x
2
)
,
{\displaystyle 4x(x+2)+3x^{2}(x+2)=(x+2)(4x+3x^{2}),\,\!}
Binomial--2 Terms
Difference of Squares , Sum of Cubes , or Difference of Cubes .Difference of Squares:
x
2
−
y
2
=
(
x
+
y
)
(
x
−
y
)
,
{\displaystyle x^{2}-y^{2}=(x+y)(x-y),\,\!}
For example:
y
2
−
9
=
(
y
+
3
)
(
y
−
3
)
,
{\displaystyle y^{2}-9=(y+3)(y-3),\,\!}
or
16
a
2
−
49
b
2
=
(
4
a
+
7
b
)
(
4
a
−
7
b
)
.
{\displaystyle 16a^{2}-49b^{2}=(4a+7b)(4a-7b).\,\!}
Sum of Cubes:
x
3
+
y
3
=
(
x
+
y
)
(
x
2
−
x
y
+
y
2
)
,
{\displaystyle x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2}),\,\!}
For example:
z
3
+
27
=
(
z
+
3
)
(
z
2
−
3
z
+
9
)
,
{\displaystyle z^{3}+27=(z+3)(z^{2}-3z+9),\,\!}
or
8
x
3
+
125
=
(
2
x
)
3
+
(
5
)
3
=
(
2
x
+
5
)
[
(
2
x
)
2
−
(
5
)
(
2
x
)
+
(
5
)
2
]
=
(
2
x
+
5
)
(
4
x
2
−
10
x
+
5
)
.
{\displaystyle 8x^{3}+125=(2x)^{3}+(5)^{3}=(2x+5)[(2x)^{2}-(5)(2x)+(5)^{2}]=(2x+5)(4x^{2}-10x+5).\,\!}
Difference of Cubes:
x
3
−
y
3
=
(
x
−
y
)
(
x
2
+
x
y
+
y
2
)
,
{\displaystyle x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2}),\,\!}
For example:
z
3
−
27
=
(
z
−
3
)
(
z
2
+
3
z
+
9
)
,
{\displaystyle z^{3}-27=(z-3)(z^{2}+3z+9),\,\!}
or
8
x
3
−
125
=
(
2
x
)
3
−
(
5
)
3
=
(
2
x
−
5
)
[
(
2
x
)
2
+
(
5
)
(
2
x
)
+
(
5
)
2
]
=
(
2
x
−
5
)
(
4
x
2
+
10
x
+
5
)
.
{\displaystyle 8x^{3}-125=(2x)^{3}-(5)^{3}=(2x-5)[(2x)^{2}+(5)(2x)+(5)^{2}]=(2x-5)(4x^{2}+10x+5).\,\!}
Trinomial
References
External links 
![{\displaystyle 8x^{3}+125=(2x)^{3}+(5)^{3}=(2x+5)[(2x)^{2}-(5)(2x)+(5)^{2}]=(2x+5)(4x^{2}-10x+5).\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d35dee388775e1870f419dbad4d1d7cc5f8d4fd)
![{\displaystyle 8x^{3}-125=(2x)^{3}-(5)^{3}=(2x-5)[(2x)^{2}+(5)(2x)+(5)^{2}]=(2x-5)(4x^{2}+10x+5).\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f72d249d76fb282ff38beda554148d02bd43855)