The numbers 1, 7, 21, 35, 35, 21, 7, 1 form a row of pascal's Triangle.

Which power of (a+b) does the row go with?
Write the next row?

I don't know lol

To determine which power of (a+b) the given row of Pascal's Triangle corresponds to, we need to observe the pattern and structure of the numbers in the row.

In Pascal's Triangle, each number in a row is obtained by summing up the two numbers directly above it from the previous row. The power of (a+b) associated with a row can be determined by the position of the row in the triangle.

For the given row, we can see that it starts with 1 and ends with 1, which are the coefficients of (a+b)^0. Based on this, we can infer that the row corresponds to the power (a+b)^0 = 1.

To write the next row of Pascal's Triangle, we simply follow the pattern of adding adjacent numbers from the previous row.

Starting with the given row: 1, 7, 21, 35, 35, 21, 7, 1
We can add adjacent numbers to form the next row:
1 + 7 = 8
7 + 21 = 28
21 + 35 = 56
35 + 35 = 70
35 + 21 = 56
21 + 7 = 28
7 + 1 = 8

Therefore, the next row of Pascal's Triangle is: 1, 8, 28, 56, 70, 56, 28, 8, 1

Signal name

easy ....

since (a+b)^n = 1a^2 + na^(n-1) b + ....

so 1, 7, 35 ... must come from (a+b)^7