Binomial expansion of (1+4x)^5 up to x^2
This question can be treated like a normal binomial expansion question which is commonly seen at A level. The standard binomial expansion is (1+x)n = 1 + nx + (n(n-1)(x2))/2! where 2! is 2 factorialSo in this question let u=4x, n=5(1+u)^5 = 1 + 5u + (5)(4)(u2)/(2)(1)(1+u)5= 1 + 5u + 10u2now we need to substitute in u=4xso (1+4x)5 = 1 (5)(4)x + 10(4x)2(1+4x)5=1+20x+160x2
