The binomial expansion

Question 1

how is Pascal’s triangle formed

Answer 1

by adding adjacent pairs of numbers to find the numbers on the next row

                               1
                           1      1
                       1      2      1
                   1     3        3     1
              1     4        6      4      1

Question 2

how to use Pascal’s triangle for coefficients when expanding

Answer 2

the (n + 1)th row of Pascal’s triangle gives the coefficients in the expansion of (a + b)^n

Question 3

factorial notation in calculator using Pascal’s triangle

Answer 3

• nCr
• (n!)/r!(n-r)!

the rth entry in the nth row of Pascal’s triangle is n-1(C)r-1= (n-1,r-1)

Question 4

why can you sometimes ignore larger powers of x

Answer 4

if x<1, x^n gets smaller as n gets larger, so you can ignore larger powers for an approximation of a function to estimate a value

Question 5

how to use Pascal’s triangle with expansion and coefficients

Answer 5

The (n+1)th row of Pascal’s triangle gives the coefficients in the expansion of (a+b)^n

Question 6

How to form Pascal’s triangle

Answer 6

Pascal’s triangle is formed by adding adjacent pairs of numbers on the next row

Question 7

Factorial notation for calculator with Pascal’s triangle

Answer 7

nCr = (n!)/r!(n-r)!
the rth entry in the nth row of Pascal’s triangle is given by n-1(C)r-1 = (n-1, r-1)

Question 8

expansion of (a+b)^n general term

Answer 8

nCr × a^n-r × b^r

Question 9

why can you sometimes ignore x with large powers in expansions

Answer 9

because if x<1, as n gets larger x^n gets smaller. Can use an approximation only using the first few terms of the function instead of a complicated expression