Question

Factories using suitable identity16x cube-2y cube

Answer 1

2(8x^3-y^3)

2{ (2x)^3-y^3}

2[ (2x-y) { (2x)^2+ y^2+ 2xy}]

Answer 2

16
x
3
−
2
y
3
16
x
3
-
2
y
3
.
Tap for fewer steps...
Factor
2
2
out of
16
x
3
16
x
3
.
2
(
8
x
3
)
−
2
y
3
2
(
8
x
3
)
-
2
y
3
Factor
2
2
out of
−
2
y
3
-
2
y
3
.
2
(
8
x
3
)
+
2
(
−
y
3
)
2
(
8
x
3
)
+
2
(
-
y
3
)
Factor
2
2
out of
2
(
8
x
3
)
+
2
(
−
y
3
)
2
(
8
x
3
)
+
2
(
-
y
3
)
.
2
(
8
x
3
−
y
3
)
2
(
8
x
3
-
y
3
)
Rewrite
8
x
3
8
x
3
as
(
2
x
)
3
(
2
x
)
3
.
2
(
(
2
x
)
3
−
y
3
)
2
(
(
2
x
)
3
-
y
3
)
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
=
2
x
a
=
2
x
and
b
=
y
b
=
y
.
2
(
(
2
x
−
y
)
(
(
2
x
)
2
+
2
x
y
+
y
2
)
)
2
(
(
2
x
-
y
)
(
(
2
x
)
2
+
2
x
y
+
y
2
)
)
Factor.
Tap for fewer steps...
Simplify.
Tap for fewer steps...
Apply the product rule to
2
x
2
x
.
2
(
(
2
x
−
y
)
(
2
2
x
2
+
2
x
y
+
y
2
)
)
2
(
(
2
x
-
y
)
(
2
2
x
2
+
2
x
y
+
y
2
)
)
Raise
2
2
to the power of
2
2
.
2
(
(
2
x
−
y
)
(
4
x
2
+
2
x
y
+
y
2
)
)
2
(
(
2
x
-
y
)
(
4
x
2
+
2
x
y
+
y
2
)
)
Remove unnecessary parentheses.
2
(
2
x
−
y
)
(
4
x
2
+
2
x
y
+
y
2
)