Binomial Expansion: Pascal Triangle, Binomial Theorem Of Negative, Positive And Fractional Power

GENERAL EVALUATION

1) Write down and simplify all the terms of the binomial expansion of ( 1 – x )⁶ . Use the expansion to evaluate  0.997⁶  correct to 4 dp

2) Write down the expansion of  ( 1 + ¼ x ) ⁵ simplifying all its coefficients

3) Use the binomial theorem to expand  ( 2 – ¼ x)⁵ and simplify all the terms

4) Deduce  the expansion of   ( 1 – x +x² )⁶  in ascending powers of x

Reading Assignment

New Further Maths Project 2  page 73 – 78

WEEKEND ASSIGNMENT

If the first three terms of the expansion of ( 1 + px )ⁿ in ascending powers of  x are   1 + 20v + 160x find  the value of

1)  n  a) 2  b) 3  c) 4  d) 5

2) p   a) 2  b) 3  c) 4  d) 5

3) In the expansion of  ( 2x + 3y )⁴  what is the coefficient of  y⁴   a) 16  b) 81  c) 216  d) 96

4) How many terms are in the expansion  of  ( 1 – 4x ) ⁵  a) 3  b) 5  c) 6  d) 8

5) What is the third term in the expansion of  ( 1 – 3x )⁶ in ascending powers of x  a) 18  b) -540  c) 135  d) 729

THEORY

1) Using binomial theorem, write down and simplify the first seven terms of the expansion of  ( 1 + 2x )¹⁰ in ascending powers of x

2) Expand  ( 2 + x )⁵ ( 1 – 2x ) ⁶ as far as the term in x³   . Evaluate  ( 1.999 )⁵ ( 1.002 )⁶