Question

Use Pascal’s triangle and binomial expansion strategies (x+y)^3

Answer 1

1. Pascal’s triangle

Pascal's triangle is an strategy in math that stands for a triangular array we use to solve problems of binomial coefficients. This strategy is called after the mathematician Blase Pascal. It consists in number patters. So in this problem we need to solve this following Pascal’s triangle strategy:

`(x+y)^3`

The strategy consists in building a triangle. So 1 is the first and last numbers in each row of Pascal’s Triangle. Next, every other number in each row is formed when you add the two numbers directly above the number, as shown in Figure below. So:

`(x+y)^3=x^3+3x^2y+3xy^2+y^3`

1. Binomial Expansion

A binomial is a polynomial having two terms. So binomial expansion is a method that stands for a formula that gives us a quick method of raising a binomial to a power. So, for n=3, the binomial expansion can be written as:

`(x+y)^3=x^3+3x^2y+3xy^2+y^3`