Binomial Theorem

The prefix bi in the words bicycle, binocular, binary and in many more words means two . The word binomial stands for expressions having two terms. For examples ( + x ) , ( x + y ) , ( x + xy ) and ( a + b ) are some binomial expressions. .

. Binomial Coefficients In Chapter we have learnt and used the symbol n C r which is defined as n C r = n ( n − )( n − ) . . .

( n − r )! r ! . Since n C r occurs as the coefficients of x r in ( + x ) n n ∈ N and as the coefficients of a r b n − r in ( a + b ) n , they are called binomial coefficients.

Though the values of n C r can be computed by formula, there is an interesting simple way to find n C r without doing cumbersome multiplications. Pascal Triangle The Pascal triangle is an arrangement of the values of n C r in a triangular form. The ( k + ) st row consists values of k C , k C , k C , k C , . .

. , k C k . In fact, the Pascal triangle is