Math, asked by areebkhan86, 9 months ago

(2x-1/x)^6 expand using binomial theorem​

Answers

Answered by lovely30mishra
0

Answer:

Use the binomial expansion theorem to find each term. The binomial theorem states

(

a

+

b

)

n

=

n

k

=

0

n

C

k

(

a

n

k

b

k

)

(a+b)n=∑k=0n⁡nCk⋅(an-kbk).

6

k

=

0

6

!

(

6

k

)

!

k

!

(

2

x

)

6

k

(

1

x

)

k

∑k=06⁡6!(6-k)!k!⋅(2x)6-k⋅(-1x)k

Expand the summation.

6

!

(

6

0

)

!

0

!

(

2

x

)

6

0

(

1

x

)

0

+

6

!

(

6

1

)

!

1

!

(

2

x

)

6

1

(

1

x

)

+

+

6

!

(

6

6

)

!

6

!

(

2

x

)

6

6

(

1

x

)

6

6!(6-0)!0!⋅(2x)6-0⋅(-1x)0+6!(6-1)!1!⋅(2x)6-1⋅(-1x)+…+6!(6-6)!6!⋅(2x)6-6⋅(-1x)6

Simplify the exponents for each term of the expansion.

1

(

2

x

)

6

(

1

x

)

0

+

6

(

2

x

)

5

(

1

x

)

+

+

1

(

2

x

)

0

(

1

x

)

6

1⋅(2x)6⋅(-1x)0+6⋅(2x)5⋅(-1x)+…+1⋅(2x)0⋅(-1x)6

Simplify the polynomial result.

64x6−192x4+240x2−160+60x2−12x4+1x6

Answered by kailashmeena123rm
2

Answer:

see attachment

Step-by-step explanation:

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