Question

Use​ Pascal's triangle to expand the binomial.
(m+n)^5

Answer 1

To expand the binomial (m+n)^5 using Pascal's Triangle, we can look at the 5th row of the triangle. Pascal's Triangle starts with the 0th row being just 1, and each subsequent row is created by adding the two numbers above it.

The 5th row of Pascal's Triangle is: 1 5 10 10 5 1

We can now use these coefficients with the variables m and n to expand the binomial:

(m+n)^5 = 1m^5 + 5m^4n + 10m^3n^2 + 10m^2n^3 + 5mn^4 + 1n^5

Therefore, the expansion of the binomial (m+n)^5 using Pascal's Triangle is:
m^5 + 5m^4n + 10m^3n^2 + 10m^2n^3 + 5mn^4 + n^5