The theorem that specifies the expansion of any power of a binomial, that is, ( a + b ) m. According to the binomial theorem, the first term of the expansion is xm , the second term is mxm&spminus;1 y, and for each additional term the power of x decreases by 1 while the power of y increases by 1, until the last term ym is reached. The coefficient of xm&spminus;r is m ![ r !( m − r )!]. Thus the expansion of ( a + b )3 is a3 + 3 a2 b + 3 ab2 + b3 .