How do I do binomial expansions for positive integer n?
The general method for (a+b)^n is: 1)write out pascals triangle (see whiteboard) and stop at the nth row. Write this on a line. 2)write down the powers of a in ascending order (and simplify) 3)write down the powers of b in descending order (and simplify) 4)multiply the first number in your 3 lines, then the second number and so on and simplify each term 5)add each term Example expand (1+3x)3 1 1 1 1 2 1 1 3 3 1 The relevant line of pascals triangle is 1,3,3,1. The powers of 1 in ascending order are just 1,1,1,1. The powers of 3x in descending order are (3x)0=1,(3x)1=3x,(3x)2=9x2,(3x)3=27x3 Our four terms are then: 111=1,31(3x)=9x, 31(9x2)=27x2, 11(27x3）=27x3 So the expansion is 1+9x+27x2+27x3
