expand (x+y)^6?

Question

how would you expand this formula? All I knowso far is that
(x+y)^6 written in binomial theorem is x^6 + (6/1)...helppp

Answer 1

x^6 + 6x^5y + 15x^4y^2 + 20x^3y^3 + 15x^2y^4 + 6xy^5 + y^6

you start with x, a coefficient of 1, to the power of 6
then subtract 1 from the power each time for x and add 1 to the power for y...x is going down, y is going up

For the coefficients, theres this pyramid thing thats helpful
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1

The first 1 is the power of 0. So like x^0 = 1
2nd is to the power of ... (x+y)^1 = 1x + 1y
3rd is (x+y)^2 ... x^2 + 2xy + y^2
....You want the last line for (x+y)^6 to get the coefficients

Hope this helps.

Oh, that actually was a pyramid when i typed it in, but when I clicked preview it didn't come out like one, but you can draw it yourself if it helps. Just put the first 1 in the middle and have everything else branch out.