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