Question

1 The coefficient of x2 in the expansion of 2x +1 by 3 whole square

Answer 1

Answer:

1 +6 x + 12 x 2 + 8x 3

Explanation:

We must use our knowledge of the binomial expansion:

Method 1:

We can use:

(

x

+

1

)

n

=

1

+

n

x

+

n

(

n

−

1

)

2

!

x

2

+

n

(

n

−

1

)

(

n

−

2

)

3

!

x

3

+

...

Substituting  

n

=

3

and  

x

for  

2

x

 

⇒

(

2

x

+

1

)

3

=

1

+

(

3

⋅

2

x

)

+

3

⋅

2

2

!

⋅

(

2

x

)

2

+

3

⋅

2

⋅

1

3

!

⋅

(

2

x

)

3

 

=

1

+

6

x

+

12

x

2

+

8

x

3

Method 2:

We can use:

(

A

+

B

)

n

=

A

n

+

(

n

1

)

A

n

−

1

B

1

+

(

n

2

)

A

n

−

2

B

2

+

...

Letting  

A

=

2

x

and

B

=

1

for this circumstance:

(

2

x

+

1

)

3

=

(

2

x

)

3

+

(

3

1

)

(

2

x

)

2

(

1

)

+

(

3

2

)

(

2

x

)

1

(

1

)

2

+

(

3

3

)

(

2

x

)

0

(

1

)

3

=

8

x

3

+

12

x

2

+

6

x

+

1

Step-by-step explanation: