Question

write down the expansions for (1+x)²​

Answer 1

Here is your answer:

Term of x

5

=

n

C

r

x

3r

(

x

2

−1

)

n−r

=

n

C

r

x

3r

.x

2r−2n

.(−1)

n−r

So 3r+2r−2n=5

r=

5

5+2n

⟶(1)

Also for x

10

be (r

1

+1)

th

term

So term with x

10

=

n

C

r

1

x

3r

1

(

x

2

−1

)

n−r

⇒3r

1

+2r

1

−2n=10

r

1

=

5

2n+10

⟶(2)

Now we know if ∣

n

C

r

∣=∣

n

C

r

1

∣⇒n=r+r

1

Now we add co oefficient of x

5

&x

10

n

C

r

(−1)

n−r

+

n

C

r

1

(−1)

n−r

1

=0

Co oefficient of x

5

is

n

C

r

(−1)

n−r

; co oeffiecient of x

10

is

n

C

r

1

(−1)

n−r

1

⇒

n

C

r

(−1)

n−r

=−(

n

C

r

1

(−1)

n−r

1

)

⇒∣

n

C

r

∣=∣

n

C

r

1

∣

So, n=r+r

1

n=

5

2n+10

+

5

2n+5

5n=4n+15

n=15

Step-by-step explanation:

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Answer 2

Answer:

(1+x)² = 1²+x²+2*1*x

= 1 + x²+ 2x

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