Math, asked by jyotsb, 2 months ago

expand:
(a+b)^3-(a-b)^3

Answers

Answered by pradipkr2910
0

Answer:

Use the Binomial expansion (note the exponents sum to the power in each term):

(

x

+

y

)

3

=

3

C

0

x

3

y

0

+

3

C

1

x

2

y

1

+

3

C

2

x

1

y

2

+

3

C

3

x

0

y

3

Remember

3

!

=

3

2

1

=

6

,

2

!

=

2

1

=

2

,

1

!

=

1

and

0

!

=

1

_

3

C

0

=

3

!

(

3

0

)

!

(

0

!

)

=

3

!

(

3

)

!

1

=

1

_

3

C

1

=

3

!

(

3

1

)

!

(

1

!

)

=

3

!

(

2

)

!

1

=

3

2

!

2

!

=

3

_

3

C

2

=

3

!

(

3

2

)

!

(

2

!

)

=

3

!

(

1

)

!

2

!

=

3

2

!

2

!

=

3

_

3

C

3

=

3

!

(

3

3

)

!

(

3

!

)

=

3

!

0

!

3

!

=

1

Note:

(

a

b

)

3

=

(

a

+

(

b

)

)

3

Substitute into the Binomial expansion formula,

let

x

=

a

and

y

=

b

:

(

a

b

)

3

=

a

3

+

3

a

2

(

b

)

1

+

3

a

(

b

)

2

+

(

b

)

3

=

a

3

3

a

2

b

+

3

a

b

2

b

3

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