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.
+310 Let's break it down and simplify each part.
(t−1)3= t3−3t2+3t−1
6(t−1)2=6(t2−2t+1)=6t2−12t+6
12(t−1)=12t−12
Combining these and the 8 together, we get our final answer: t3−3t2+3t−1 +6t2−12t+6 +12t−12+8 = t3+3t2−3t+1
