12 x1 t08 01 binomial expansions (2012)

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  • 1. Binomial Theorem

2. Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms. 3. Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms. 1 x 0 1 4. Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms. 1 x 0 11 x 1 1 1x 5. Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms. 1 x 0 1 1 x 1 1 1x1 x 2 1 2 x 1x 2 6. Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms. 1 x 0 1 1 x 1 1 1x1 x 2 1 2 x 1x 21 x 1 x 1 2 x 1x 2 3 1 2 x x 2 x 2 x 2 x3 1 3x 3x 2 x 3 7. Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms. 1 x 0 1 1 x 1 1 1x1 x 2 1 2 x 1x 21 x 1 x 1 2 x 1x 2 3 1 2 x x 2 x 2 x 2 x3 1 3x 3x 2 x 31 x 4 1 x 1 3x 3x 2 x 3 1 3x 3x 2 x 3 x 3x 2 3x 3 x 4 1 4 x 6 x 2 4 x3 x 4 8. Blaise Pascal saw a pattern which we now know as Pascals Triangle 9. Blaise Pascal saw a pattern which we now know as Pascals Triangle 1 10. Blaise Pascal saw a pattern which we now know as Pascals Triangle 1 1 1 11. Blaise Pascal saw a pattern which we now know as Pascals Triangle 1 1 1 1 2 1 12. Blaise Pascal saw a pattern which we now know as Pascals Triangle11 11 2 11 3 3 1 13. Blaise Pascal saw a pattern which we now know as Pascals Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 14. Blaise Pascal saw a pattern which we now know as Pascals Triangle1 11 121 1 331 1 464 1 1 5 10 10 5 1 15. Blaise Pascal saw a pattern which we now know as Pascals Triangle1 1 11 2 113 3 11 4 6 411 510105 11 6 152015 6 1 16. Blaise Pascal saw a pattern which we now know as Pascals Triangle 11 1 1 2 11 3 3 114 6 4 11 5 1010511 61520156 11 7 21353521 7 1 17. Blaise Pascal saw a pattern which we now know as Pascals Triangle 11 1 1 2 11 3 3 1 1 4 6 4 1 15 10105 1 1 6 15201561 1 7213535217 1 1 8 2856705628 8 1 18. Blaise Pascal saw a pattern which we now know as Pascals Triangle1 1 11 2 1 1 3 3 1 14 6 4 1 1 5 101051 1 61520156 1 1 7 21353521 7 1 1 8 285670 5628 8 1 1 9 36 84126 12684 36 9 1 19. Blaise Pascal saw a pattern which we now know as Pascals Triangle1 1 11 2 1 1 3 3 1 14 6 4 1 1 5 101051 1 61520156 1 1 7 21353521 7 1 128 85670 5628 8 11936 84126 12684 36 9 1 1 10 45 120 210 252 210 120 45 10 1 20. 7 2x e.g .i 1 3 21. 7 2x e.g .i 1 32 34 5 17 71 211 351 351 211 6 2x5 2x4 2x3 2x2 2x 3 3 3 3 36 7 2x 2x 71 3 3 22. 7 2x e.g .i 1 32 3 45 17 71 211 351 351 211 6 2x5 2x4 2x3 2x2 2x 3 3 3 3 36 7 2x 2x 71 3 314 x 84 x 2 280 x 3 560 x 4 672 x 5 448 x 6 128 x 7 1 3 9 2781 243 729 2187 23. 7 2x e.g .i 1 3 2 3 45 17 71 211 351 351 211 6 2x5 2x4 2x3 2x2 2x 3 3 3 3 3 6 7 2x 2x 71 3 3 14 x 84 x 2 280 x 3 560 x 4 672 x 5 448 x 6 128 x 7 1 3 9 2781 243 729 2187ii Use the expansion of 1 x 10 to find the value of 0.99810 to 8 dps 24. 7 1 2 x e.g .i 3 2 3 45 17 71 211 351 351 211 6 2x5 2x4 2x3 2x2 2x 3 3 3 3 3 67 2x 2x 71 3 3 14 x 84 x 2 280 x 3 560 x 4 672 x 5 448 x 6 128 x 7 1 3 9 2781 243 729 2187ii Use the expansion of 1 x 10 to find the value of 0.99810 to 8 dps 1 x 10 1 10 x 45 x 2 120 x 3 210 x 4 252 x 5 210 x 6 120 x 7 45 x8 10 x 9 x10 25. 7 1 2 x e.g .i 3 2 3 45 17 71 211 351 351 211 6 2x5 2x4 2x3 2x2 2x 3 3 3 3 3 67 2x 2x 71 3 3 14 x 84 x 2 280 x 3 560 x 4 672 x 5 448 x 6 128 x 7 1 3 9 2781 243 729 2187ii Use the expansion of 1 x 10 to find the value of 0.99810 to 8 dps 1 x 10 1 10 x 45 x 2 120 x 3 210 x 4 252 x 5 210 x 6 120 x 7 45 x8 10 x 9 x10 0.99810 1 100.002 450.0022 1200.0023 26. 7 1 2 x e.g .i 3 2 34 5 17 71 211 351 351 211 6 2x5 2x4 2x3 2x2 2x 3 3 3 3 3 67 2x 2x 71 3 3 14 x 84 x 2 280 x 3 560 x 4 672 x 5 448 x 6 128 x 7 1 3 9 2781 243 729 2187ii Use the expansion of 1 x 10 to find the value of 0.99810 to 8 dps 1 x 10 1 10 x 45 x 2 120 x 3 210 x 4 252 x 5 210 x 6 120 x 7 45 x8 10 x 9 x10 0.998 1 100.002 450.002 1200.002 1023 0.98017904 27. iii Find the coefficient of x 2 in 2 3x 4 5 x 4 28. iii Find the coefficient of x 2 in 2 3x 4 5 x 4 2 3x 4 5 x 4 2 3 x 44 443 5x 642 5x 2 445x 3 5x 4 29. iii Find the coefficient of x 2 in 2 3x 4 5 x 4 2 3x 4 5 x 4 2 3 x 44 443 5x 642 5x 2 445x 3 5x 4 30. iii Find the coefficient of x 2 in 2 3x 4 5 x 4 2 3x 4 5 x 4 2 3 x 44 443 5x 642 5x 2 445x 3 5x 4 31. iii Find the coefficient of x 2 in 2 3x 4 5 x 4 2 3x 4 5 x 4 2 3 x 44 443 5x 642 5x 2 445x 3 5x 4 coefficient of x 2 26 4 5 34 4 5 2 23 32. iii Find the coefficient of x 2 in 2 3x 4 5 x 4 2 3x 4 5 x 4 2 3 x 44 443 5x 642 5x 2 445x 3 5x 4 coefficient of x 2 26 4 5 34 4 5 2 23 4800 3840 960 33. iii Find the coefficient of x 2 in 2 3x 4 5 x 4 2 3x 4 5 x 4 2 3 x 44 443 5x 642 5x 2 445x 3 5x 4 coefficient of x 2 26 4 5 34 4 5 2 23 4800 3840 960Exercise 5A; 2ace etc, 4, 6, 7, 9ad, 12b, 13ac, 14ace, 16a, 22, 23