The Binomial Expansion

The Binomial Expansion

Use the binomial expansion (a + b)n = to expand each of the following binomials.

1. (x + 2y)5 2. (2x – y)4

3. (3x – 5y)4 4. (2x + 5y)7

5. Find the fourth term in the expansion of (2x – 3y)7.

6. Find the sixth term in the expansion of (4x + 3y)12.

7. Find the fourteenth term in the expansion of (3x + 5y)27.

8. Find the ninth term in the expansion of (4x – 6y)11.

9. Find the tenth term in the expansion of (4x – 5y)17.

10. Find the seventeenth term in the expansion of (3x – 2y)20.

11. Find the twelfth term in the expansion of (3x – y)16.

12. Find the eighth term in the expansion of (2x – 5y)12.

13. Find the fourth term of .

14. Find the fifth term of .

15. Find the fourth term of ( – x–1)8.

16. Find the sixth term of .

17. Find the sixth term of .

18. Find the fifth term of .

19. Find the fifth term of .

20. Find second term of (x + y )9.

21. Find the seventh term of .

22. Find the third and fourth terms of .

23. Find, in simplest form, (–1 + 2i)3 where i = .

24. Find the value of ( – )5.

25. Find and simplify the first four terms of .

26. Find the value of (1 – i)5 where i = .

27. Find the first three terms of .

28. Find the first five terms of (3 – 2 )7.

29. Find the first three terms of .

30. Find the third term of ( – x)6.

Answers

5. –15120x4y3 6. 3153199104x7y5

7. 11711209361901855467500x14y13 8. 17736744960x3y8

9. –3111680000000000x8y9 10. 25719275520x4y16

11. –1061424x5y11 12. –1980000000x5y7

13. – 14. 15. –

16. – 231 17. –252 18.

19. 70 20. 126y7x 21. 28

22. – , 23. 11 – 2i 24. 89 – 109

25. – + – 7x 26. –4 + 4i

27. a12 – 16a10 + 112a8 28. –128x + 1344x3 – 6048x + 15120x2 – 2268x

29. x9y–3 – 12x8y + 60x7y2 30. –