Question

expand (x square -y)³

​

Answer 1

ANSWER

=(1+x

2

)

4

(1+x

3

)

7

(1+x

4

)

12

=(

4

C

0

+

4

C

1

x

2

+

4

C

2

x

4

+

4

C

3

x

6

+

4

C

4

x

8

)(

7

C

0

+

7

C

1

x

3

+

7

C

2

x

6

+

7

C

3

x

9

+.......+

7

C

7

x

21

)

×(

12

C

0

+

12

C

1

x

4

+

12

C

2

x

8

+........+

12

C

12

x

48

)

required power of x is 11

⇒x

(2l+3m+4n)

=x

11

⇒(2l,3m,4n)≡(0,3,8);(2,9,0);(4,3,4);(8,3,0)

⇒(l,m,n)≡(0,1,2);(1,3,0);(2,1,1);(4,1,0)

Calculation of coefficient of x

11

=(

4

C

0

×

7

C

1

×

12

C

2

)+(

4

C

1

×

7

C

3

×

12

C

0

)+(

4

C

2

×

7

C

1

×

12

C

1

)+(

4

C

4

×

7

C

1

×1)

=(1×7×66)+(4×35×1)+(6×7×12)+(1×7)=462+140+504+7=1113.