Bionomial Expansion and Pascal's Triangle

Bionomial Expansion describes the algebraic expansion of powers of a binomial. A binomial is the sum of two monomials; algebraic expression consisting of a single term such as x.

The most basic formula of binomial expansion is (x+y)². This can be found using Pascal's triangle which gives the coefficient of the x and y values.

(x+y)²=x²+2xy+y².

Notice that in the first term there is no y value i.e y⁰.

From that point which each term the power of x decreases by 1 and the power of y increases by 1. Although Pascal’s triangle is attributed to Blaise Pascal who described them in the 17th century this special case of binomial expansion was first spotted by the 4th century BC Greek mathematician Euclid.

For a binomial involving subtraction Pascal's triangle can still be applied as long as the opposite of the second term is used. This makes every other term negative;

Pascal's Triangle