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We can use the right outside diagonal of the empty Calpas's triangle as the coefficients of a polynomial: t^3 + 6t^2 + 12t + 8. If we replace every t with t-1, we get (t-1)^3 + 6(t-1)^2 + 12(t-1) + 8. Expand and simplify this polynomial. Enter the polynomial as your answer.

 Jun 14, 2020
 #1
avatar+310 
+1

Let's break it down and simplify each part.

(t1)3t33t2+3t1

6(t1)2=6(t22t+1)=6t212t+6

12(t1)=12t12

Combining these and the 8 together, we get our final answer: t33t2+3t1 +6t212t+6 +12t12+8 =  t3+3t23t+1

 Jun 14, 2020
edited by thelizzybeth  Jun 14, 2020
 #2
avatar+1262 
+2

I agree with tizzlybeth that it is t^3+3t^3+3t+1 

jimkey17  Jun 20, 2020
edited by jimkey17  Jun 22, 2020

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