The Binomial Theorem 6f2l4a

Kuta Software - Infinite Algebra 2

Name___________________________________

The Binomial Theorem

Date________________ Period____

Find each coefficient described. 1) Coefficient of x 2 in expansion of (2 + x)

3) Coefficient of x in expansion of ( x + 3)

5

2) Coefficient of x 2 in expansion of ( x + 2)

5

4) Coefficient of b in expansion of (3 + b)

5) Coefficient of x 3 y 2 in expansion of ( x − 3 y)

7) Coefficient of a 2 b 2 in expansion of (a − b)

4

5

5

4

6) Coefficient of a 2 in expansion of (2a + 1)

5

8) Coefficient of m 3 n 2 in expansion of (m + 3n)

5

Find each term described. 9) 2nd term in expansion of ( y − 2 x) 4

11) 2nd term in expansion of (3u − 1)

10) 4th term in expansion of (4 y + x) 4

3

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12) 3rd term in expansion of ( y − 4)

-1-

3

Worksheet by Kuta Software LLC

13) 1st term in expansion of (a + b)

5

14) 2nd term in expansion of ( y − x)

4

Expand completely. 15) (2n + 1) 5

17) (2m − 1)

4

19) (v − 2) 3

21) ( x 4 − y)

16) ( x + y) 4

18) ( x − 3 y)

5

20) ( x − y) 3

5

23) ( y − x 2 ) 3

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22) (2 x 3 + 1)

5

24) ( y 3 − 4 x) 3

-2-

Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Name___________________________________

The Binomial Theorem

Date________________ Period____

Find each coefficient described. 1) Coefficient of x 2 in expansion of (2 + x)

5

2) Coefficient of x 2 in expansion of ( x + 2)

80

5

80

3) Coefficient of x in expansion of ( x + 3)

5

4) Coefficient of b in expansion of (3 + b)

405

4

108

5) Coefficient of x 3 y 2 in expansion of ( x − 3 y)

5

6) Coefficient of a 2 in expansion of (2a + 1)

90

5

40

7) Coefficient of a 2 b 2 in expansion of (a − b)

4

8) Coefficient of m 3 n 2 in expansion of (m + 3n)

6

5

90

Find each term described. 9) 2nd term in expansion of ( y − 2 x) 4

10) 4th term in expansion of (4 y + x) 4

−8 y 3 x

11) 2nd term in expansion of (3u − 1)

16 yx 3

3

12) 3rd term in expansion of ( y − 4)

−27u 2

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3

48 y

-1-

Worksheet by Kuta Software LLC

13) 1st term in expansion of (a + b)

5

14) 2nd term in expansion of ( y − x)

a5

4

−4 y 3 x

Expand completely. 15) (2n + 1) 5

16) ( x + y) 4

32n 5 + 80n 4 + 80n 3 + 40n 2 + 10n + 1

17) (2m − 1)

4

x 4 + 4 x 3 y + 6 x 2 y 2 + 4 xy 3 + y 4

18) ( x − 3 y)

16m 4 − 32m 3 + 24m 2 − 8m + 1

19) (v − 2) 3

x 5 − 15 x 4 y + 90 x 3 y 2 − 270 x 2 y 3 + 405 xy 4 − 243 y 5

20) ( x − y) 3

v 3 − 6v 2 + 12v − 8

21) ( x 4 − y)

5

5

x 3 − 3 x 2 y + 3 xy 2 − y 3

22) (2 x 3 + 1)

x 20 − 5 x 16 y + 10 x 12 y 2 − 10 x 8 y 3 + 5 x 4 y 4 − y 5

23) ( y − x 2 ) 3

5

32 x 15 + 80 x 12 + 80 x 9 + 40 x 6 + 10 x 3 + 1

24) ( y 3 − 4 x) 3

y 3 − 3 y 2 x 2 + 3 yx 4 − x 6

y 9 − 12 y 6 x + 48 y 3 x 2 − 64 x 3

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-2-

Worksheet by Kuta Software LLC