Core 4 - Binomial Expansion

Question 1

Give the general formula for the binomial expansion of (1+x)^n

Answer 1

1+nx+((n(n-1))/2)x^2 + (((n(n-1)*(n-2))/6)x^3 + ….

Question 2

What must you do when you need to expand (3+3x)^1/2

Answer 2

Take a factor of 3 outside the bracket to make it (1+x), then raise the multiplier to the power = 3^1/2.

Question 3

How do you approach this question

Having found the expansion of (1-2x)^-3, now find the result of (2-2x)/(1-2x)^3

Answer 3

This is the same as (2-2x)*(1-2x)^-3, so multiply the expansion by the first bracket, discounting all results greater than the power required.

Question 4

Which power of x does the co-efficient including 2! go with?

Answer 4

x^2

Question 5

Which power of x does the co-efficient including 3! go with?

Answer 5

x^3

Question 6

What must the integer in the bracket be in order to expand binomially?

Answer 6

1

Question 7

If the integer is not 1 in the bracket, how do you modify the expansion?

use the example (4+3x)^0.5

Answer 7

Take the factor out of the bracket, in order to make the integer zero, remembering to multiply the x co-efficient appropriately. Take the factor to the power of the exponent of the bracket.

2(1+3x/4)^0.5

Question 8

When modifying (1+x)^n to (1+3x)^n, what must you remember?

Answer 8

The 3x must be inside the brackets, so it becomes (3x)^2 for the x^2 term = 9x^2