What is the bionominal expansion of (x+2y)^7
1 answer:
Answer:
Choose the 8th row of Pascal's triangle to get the sequence:
1
,
7
,
21
,
35
,
35
,
21
,
7
,
1
Write the powers of
2
in ascending order up to
2
7
as a sequence:
1
,
2
,
4
,
8
,
16
,
32
,
64
,
128
Multiply the two sequences together to get:
1
,
14
,
84
,
280
,
560
,
672
,
448
,
128
Then:
(
x
+
2
y
)
7
=
x
7
+
14
x
6
y
+
84
x
5
y
2
+
280
x
4
y
3
+
560
x
3
y
4
+
672
x
2
y
5
+
448
x
y
6
+
128
y
7
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