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Cube of Difference
Reference
> Algebra: Sums and Differences of Squares and Cubes
Description
The Cube of Difference Rule states that:
(
a
−
b
)
3
=
a
3
−
3
a
2
b
+
3
a
b
2
−
b
3
{(a-b)}^{3}={a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}
(
a
−
b
)
3
=
a
3
−
3
a
2
b
+
3
a
b
2
−
b
3
Examples
x
3
−
6
x
2
+
12
x
−
8
{x}^{3}-6{x}^{2}+12x-8
x
3
−
6
x
2
+
1
2
x
−
8
1
Rewrite it in the form
a
3
−
3
a
2
b
+
3
a
b
2
−
b
3
{a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}
a
3
−
3
a
2
b
+
3
a
b
2
−
b
3
, where
a
=
x
a=x
a
=
x
and
b
=
2
b=2
b
=
2
.
x
3
−
3
x
2
(
2
)
+
3
(
x
)
×
2
2
−
2
3
{x}^{3}-3{x}^{2}(2)+3(x)\times {2}^{2}-{2}^{3}
x
3
−
3
x
2
(
2
)
+
3
(
x
)
×
2
2
−
2
3
2
Use
Cube of Difference
:
(
a
−
b
)
3
=
a
3
−
3
a
2
b
+
3
a
b
2
−
b
3
{(a-b)}^{3}={a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}
(
a
−
b
)
3
=
a
3
−
3
a
2
b
+
3
a
b
2
−
b
3
.
(
x
−
2
)
3
{(x-2)}^{3}
(
x
−
2
)
3
Done
(x-2)^3
English
Cube of Difference