Which ones are correct check all that apply

Pascal's triangle is a pyramid shape of numbers such that

row1: only has the number 1 in it
row2: has the numbers 1,1 in it
row3: has the numbers 1,2,1 in it
row4: has the numbers 1,3,3,1 in it
row5: has the numbers 1,4,6,4,1
row6: has the numbers 1,5,10,10,5,1

and so on. I recommend looking at the triangle itself to get a better idea how it's shaped. Each row has a 1 in the beginning and a 1 at the end. So choice C is true. Furthermore, the nth row corresponds to the expansion of (x+y)^(n-1)

For example, if n = 3, then

(x+y)^(n-1) = (x+y)^(3-1)
(x+y)^(n-1) = (x+y)^2
(x+y)^(n-1) = 1x^2+2xy+1y^2

Or another example, if n = 4, then 

(x+y)^(n-1) = (x+y)^(4-1) 
(x+y)^(n-1) = (x+y)^3
(x+y)^(n-1) = 1x^3+3x^2y+3xy^2+1y^3

and so on. Which is why choice A is true.



The final answer is that choice A and choice C are true.

Note: Choices B and D are false. B is false because the numbers are the sum of the values above. D is false since it contradicts choice A. 

Step-by-step explanation:

(a - b)² = a² + 2ab + b²

Area of square frame =side²

                                   = (2b - 1)²

                                   = (2b)² - 2*2b * 1 + 1²

                                   = 4b² - 4b + 1