54x
(a
Answers
Answered by
0
Answer:
Explanation:
When factoring,
Step 1: Always factor out a GCF first, if possible.
In this particular problem, we can factor out 2:
54
x
3
−
2
y
3
=
2
(
27
x
3
−
y
3
)
Step 2: Count the number of terms:
—if 2 terms, check if problem is:
difference of squares
(
a
2
−
b
2
)
, which factors into
(
a
−
b
)
(
a
+
b
)
difference of cubes
(
a
3
−
b
3
)
, which factors into
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
sum of cubes
(
a
3
+
b
3
)
, which factors into
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
(
27
x
3
−
y
3
)
is a difference of cubes:
27
x
3
=
(
3
x
)
3
y
3
=
(
y
)
3
Plugging these values into the difference of cubes formula:
(
a
3
−
b
3
)
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
(
(
3
x
)
3
−
(
(
y
)
3
)
=
(
(
3
x
)
−
(
y
)
)
(
(
3
x
)
2
+
(
3
x
)
(
y
)
+
(
y
)
2
)
27
x
3
−
y
3
=
(
3
x
−
y
)
(
9
x
2
+
3
x
y
+
y
2
)
Putting it all together:
54
x
3
−
2
y
3
=
2
(
27
x
3
−
y
3
)
54
x
3
−
2
y
3
=
2
(
3
x
−
y
)
(
9
x
2
+
3
x
y
+
y
2
)
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