polynomial expansion

Question 1

formula booklet formulae

Answer 1

Question 2

how to find the Pascal’s triangle multiplier bit

Answer 2

nCr function

nCr = n! ÷ ( r! (n-r)! )

n is the power
r is the term

Question 3

expand (a+bx)^n, giving your answer in ascending powers of x

Answer 3

= (nC0) × (a)^n × (bx)^0
+ (nC1) × (a)^(n-1) × (bx)^1
+ (nC2) × (a)^(n-2) × (bx)^2
+ …
+ (nCn) × (a)^(0) × (bx)^n

** Ensure the powers sum to n

Question 4

(1+2x)⁸ ≈ 1 + 16x + 112x²
Use to find an approximation for 1.02⁸

Answer 4

When x is small,, x² is very small. Any subsequent powers become negligible

Let (1+2x)⁸ = 1.02⁸
1+2x = 1.02
2x = 0.02
plug in x = 0.01 and solve

Question 5

only equate polynomial approximations if

Answer 5

both are to the same power