Question

Using Pascal's Triangle, expand (x+3y)^3 and (m+3n)^3. Show work.

Answer 1

(a + b)^3 = a^3 + 3(a^2)b + 3a(b^2) + b^3. For the first problem a = x and b = 3y. Similar for the second with a change of variables.

Answer 2

So far I have x^3+9x^2y but I'm not sure what else to do.

Answer 3

Hold on and I'll upload a picture.

Answer 4

This what I have so far.

Answer 5

You're on the right track, but you need to be including the "3" when you are putting an exponent on "y". It is NOT understood to extend to the 3. 3y^2 is not the same as (3y)^2. That will mess you up eventually and is wrong notation. Use the parentheses.

Answer 6

So, do I square 3 which gives me 9 then multiply it by 3 to get 27?

Then I would have x^3+9x^2y+27xy^2 so far right?

Answer 7

Absolutely correct! You are understanding this well. It's just your notation that was a little off before. I think you are solidly on track now.

Answer 8

Is the final answer x^3+9x^2y+27xy^2+27y^3?

Answer 9

You're right there! 100% ! I've helped you on a different question and you do very well. Good work!

Answer 10

Thank you!

Answer 11

You are quite welcome!