Question

What is the bionominal expansion of (x+2y)^7

Answer 1

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