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Algebra Examples
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Algebra
Factor 27-x^3
27
−
x
3
27
-
x
3
Step 1
Rewrite
27
27
as
3
3
3
3
.
3
3
−
x
3
3
3
-
x
3
Step 2
Since both
terms
are perfect
cubes
,
factor
using the
difference of cubes
formula
,
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
a
3
-
b
3
=
(
a
-
b
)
(
a
2
+
a
b
+
b
2
)
where
a
=
3
a
=
3
and
b
=
x
b
=
x
.
(
3
−
x
)
(
3
2
+
3
x
+
x
2
)
(
3
-
x
)
(
3
2
+
3
x
+
x
2
)
Step 3
Raise
3
3
to the
power
of
2
2
.
(
3
−
x
)
(
9
+
3
x
+
x
2
)
(
3
-
x
)
(
9
+
3
x
+
x
2
)
2
7
−
x
3
2
7
-
x
3
(
(
)
)
|
|
[
[
]
]
√
√
≥
≥
7
7
8
8
9
9
≤
≤
4
4
5
5
6
6
/
/
^
^
×
×
>
>
∩
∩
∪
∪
1
1
2
2
3
3
-
-
+
+
÷
÷
<
<
π
π
∞
∞
,
,
0
0
.
.
%
%
=
=
⎡
⎢
⎣
x
2
1
2
√
π
∫
x
d
x
⎤
⎥
⎦
[
x
2
1
2
π
∫
x
d
x
]
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