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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+307 
+2

Let's break it down and simplify each part.

\((t-1)^3\)\(t^3-3t^2+3t-1\)

\(6(t-1)^2\)\( = 6(t^2-2t+1) = 6t^2-12t+6\)

\(12(t-1)=12t-12\)

Combining these and the 8 together, we get our final answer: \(t^3-3t^2+3t-1\) \( + 6t^2-12t+6\) \( + 12t-12+8\) =  \(t^3+3t^2-3t+1\)

 Jun 14, 2020
edited by thelizzybeth  Jun 14, 2020
 #2
avatar+1130 
+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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