How do you expand $(r+3)^5$ using Pascal’s Triangle?

Question

7113 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-09T08:09:27

See below

Look at 5th row in Pascal' triangle (1, 5, 10, etc)
enter image source here

Then the Binomial theorem applyed to this case

$(r+3)^5=1·r^5·3^0+5·r^4·3+10·r^3·3^2+10·r^2·3^3+5·r^1·3^4+1·r^0·3^5=r^5+15r^4+90r^3+90r^2+135r+243$

How do you expand (r+3)^5(r+3)^5 using Pascal’s Triangle?