Binomial Expansion B1 Ch8

Question 1

What can be used to show binomial expansions?

Answer 1

Pascal’s triangle

Question 2

How can Pascal’s triangle be used for working out binomial expansions

Answer 2

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

Question 3

What does 3! mean?

Answer 3

3x2x1

Question 4

How is factorial notation written?

Answer 4

nCr or (n) (r)

Question 5

What is the formula for n choose r?

Answer 5

n!/r!(n-r)!

Question 6

How can any number in Pascal’s triangle be found

Answer 6

n-1Cr-1 or (n-1) (r-1) For the rth entry into the nth row of Pascal’s triangle

Question 7

How would you expand (3-2x)⁵

Answer 7

5C0 x 3⁵ + 5C1 x 3⁴(-2x) + 5C2 x 3³(-2x)² + 5C3 x 3²(-2x)³ + 5C4 x 3¹(-2x)⁴ + 5C5 x (-2x)⁵

Question 8

How can individual coefficients in a binomial expansion be found?

Answer 8

In the expansion of (a+b)ⁿ the general term is given (n)a^(n-r)b^r

Question 9

Find the coefficient of the x⁴ term in the binomial expansion of (2+3x)¹⁰

Answer 9

10C4 x 2⁶(3x)⁴=1088640x⁴

Question 10

When are binomial estimations used?

Answer 10

When x is less than 1 so large powers of x can be ignored