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8
x
3
−
125
8{x}^{3}-125
8
x
3
−
1
2
5
+
−
.
ln
>
<
×
÷
/
log
≥
≤
(
)
log
x
=
%
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factor(8x^3-125)
factor 8x^3-125
{8x}^{3}-125
1
Rewrite it in the form
a
3
−
b
3
{a}^{3}-{b}^{3}
a
3
−
b
3
, where
a
=
2
x
a=2x
a
=
2
x
and
b
=
5
b=5
b
=
5
.
(
2
x
)
3
−
5
3
{(2x)}^{3}-{5}^{3}
(
2
x
)
3
−
5
3
2
Use
Difference of Cubes
:
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
{a}^{3}-{b}^{3}=(a-b)({a}^{2}+ab+{b}^{2})
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
.
(
2
x
−
5
)
(
(
2
x
)
2
+
(
2
x
)
(
5
)
+
5
2
)
(2x-5)({(2x)}^{2}+(2x)(5)+{5}^{2})
(
2
x
−
5
)
(
(
2
x
)
2
+
(
2
x
)
(
5
)
+
5
2
)
3
Use
Multiplication Distributive Property
:
(
x
y
)
a
=
x
a
y
a
{(xy)}^{a}={x}^{a}{y}^{a}
(
x
y
)
a
=
x
a
y
a
.
(
2
x
−
5
)
(
2
2
x
2
+
2
x
×
5
+
5
2
)
(2x-5)({2}^{2}{x}^{2}+2x\times 5+{5}^{2})
(
2
x
−
5
)
(
2
2
x
2
+
2
x
×
5
+
5
2
)
4
Simplify
2
2
{2}^{2}
2
2
to
4
4
4
.
(
2
x
−
5
)
(
4
x
2
+
2
x
×
5
+
5
2
)
(2x-5)(4{x}^{2}+2x\times 5+{5}^{2})
(
2
x
−
5
)
(
4
x
2
+
2
x
×
5
+
5
2
)
5
Simplify
5
2
{5}^{2}
5
2
to
25
25
2
5
.
(
2
x
−
5
)
(
4
x
2
+
2
x
×
5
+
25
)
(2x-5)(4{x}^{2}+2x\times 5+25)
(
2
x
−
5
)
(
4
x
2
+
2
x
×
5
+
2
5
)
6
Simplify
2
x
×
5
2x\times 5
2
x
×
5
to
10
x
10x
1
0
x
.
(
2
x
−
5
)
(
4
x
2
+
10
x
+
25
)
(2x-5)(4{x}^{2}+10x+25)
(
2
x
−
5
)
(
4
x
2
+
1
0
x
+
2
5
)
Done
(2*x-5)*(4*x^2+10*x+25)
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