how do you solve (x+y)^4, using some pyramind thing....?

Question

its this pyramind that helps you solve problems like this it goes something like this:
1
11
121
.....

that is all i know i need to know whole pyramind up to the 12th row please help me

Answer 1

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
1,7, 21,35,35,21,7,1
1,8,28,56,70,56,28,8,1
1,9,36,84,126,126,84,36,9,1
1,10,45,120,210,252,210,120,45
10,1
1,11,55,165,330,462,462,330
165,55,11,1
1,12,66,220,495,792,924,792,
495,220,66,12,1


1(x^4)+ 4(x^3y)+6(x^2y^2)+

4(xy^3)+1(y^4)

Answer 2

0 = 1
1 = 1 1
2 = 1 2 1
3 = 1 3 3 1
4 = 1 4 6 4 1

therefore (x+y)^4 = x^4 + 4x^3 * y + 6x^2 * y^2 +4x * y^3 +y^4

so that pyramis thing gives you the coefficients for this pattern

by the way if you don't understand the pyramid pattern, you get every number by adding the two numbers on top of it. So teh next line will be 1 5 10 10 5 1 because 0+1 = 1, 1+4 = 5, 4+6= 10, 6+4=10, 4+1 = 5, and 1+0=1

Answer 3

That array is called Pascal's Triangle. Each subsequent row contains one more entry than the previous row. Each row begins and ends with 1. Other elements in the row are always the sum of the two entries above it.

Thus, the next row is 1 3 3 1, next is 1 4 6 4 1, then 1 5 10 10 5 1, and so on.

The n-th row gives the coefficients in the expansion of
(x + y)^n.

Answer 4

Pascal Triangle

1
11
121
1331
14641
........

(x+y)^4
1x^4y^0 + 4x^3y^1 + 6x^2y^2 + 4x^1y^3 +1x^0y^4


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x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4