Pascal’s Triangle and Binomial theorem

An algebraic expression containing two terms is called binomial expression. The general form of the binomial expression is (x+a) and the expansion of (x+a)^n, where n is a natural number, is called binomial theorem. It gives a formula for the expansion of the powers of binomial expression.
The coefficients in the binomial expansion follow a specific pattern known as Pascal’s triangle.
Following are some important features of Pascal’s triangle.
-Each row is bounded by 1 on both sides.
-Any entry except first and last, is the sum of two entries in preceding row , one on the immediate left and other on immediate right.
Some important conclusions from the Binomial Theorem:
Total number of terms in binomial expansion is n+1.
The coefficients of terms equidistant from the beginning and end are equal. These coefficients are known as binomial coefficients.
The terms in the expansion of (x-a)^n are alternatively positive and negative first being positive always.
The coefficient of x^r in (r+1)th term in the expansion of (x+a)^n is (_r^n)C.
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