Factored Expansion 0

y = [\begin{matrix} \frac{1}{1} \end{matrix}] \cdot [\begin{matrix} y_{0} \end{matrix}]

y = [\begin{matrix} \frac{1}{2} & \frac{1}{2} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \end{matrix}]

y = [\begin{matrix} 1 - x & x \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \end{matrix}]

y = [\begin{matrix} \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \end{matrix}]

y = [\begin{matrix} \frac{- (3 x - 5)}{6} & \frac{1}{3} & \frac{3 x - 1}{6} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \end{matrix}]

y = [\begin{matrix} \frac{x^{2} - 3 x + 2}{2} & - x (x - 2) & \frac{x (x - 1)}{2} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \end{matrix}]

y = [\begin{matrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \\ y_{3} \end{matrix}]

y = [\begin{matrix} \frac{- (3 x - 7)}{10} & \frac{- (x - 4)}{10} & \frac{x + 1}{10} & \frac{3 x - 2}{10} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \\ y_{3} \end{matrix}]

y = [\begin{matrix} \frac{5 x^{2} - 21 x + 19}{20} & \frac{- (5 x^{2} - 13 x - 3)}{20} & \frac{- (5 x^{2} - 17 x + 3)}{20} & \frac{5 x^{2} - 9 x + 1}{20} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \\ y_{3} \end{matrix}]

y = [\begin{matrix} \frac{- (x^{3} - 6 x^{2} + 11 x - 6)}{6} & \frac{x (x^{2} - 5 x + 6)}{2} & \frac{- x (x^{2} - 4 x + 3)}{2} & \frac{x (x^{2} - 3 x + 2)}{6} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \\ y_{3} \end{matrix}]

y = [\begin{matrix} \frac{1}{5} & \frac{1}{5} & \frac{1}{5} & \frac{1}{5} & \frac{1}{5} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \\ y_{3} \\ y_{4} \end{matrix}]

y = [\begin{matrix} \frac{- (x - 3)}{5} & \frac{- (x - 4)}{10} & \frac{1}{5} & \frac{x}{10} & \frac{x - 1}{5} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \\ y_{3} \\ y_{4} \end{matrix}]

y = [\begin{matrix} \frac{5 x^{2} - 27 x + 31}{35} & \frac{- (5 x^{2} - 13 x - 18)}{70} & \frac{- (5 x^{2} - 20 x + 3)}{35} & \frac{- (5 x^{2} - 27 x + 10)}{70} & \frac{5 x^{2} - 13 x + 3}{35} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \\ y_{3} \\ y_{4} \end{matrix}]

y = [\begin{matrix} \frac{- (35 x^{3} - 270 x^{2} + 625 x - 414)}{420} & \frac{35 x^{3} - 225 x^{2} + 340 x + 12}{210} & \frac{- (5 x^{2} - 20 x + 3)}{35} & \frac{- (35 x^{3} - 195 x^{2} + 220 x - 12)}{210} & \frac{35 x^{3} - 150 x^{2} + 145 x - 6}{420} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \\ y_{3} \\ y_{4} \end{matrix}]

y = [\begin{matrix} \frac{x^{4} - 10 x^{3} + 35 x^{2} - 50 x + 24}{24} & \frac{- x (x^{3} - 9 x^{2} + 26 x - 24)}{6} & \frac{x (x^{3} - 8 x^{2} + 19 x - 12)}{4} & \frac{- x (x^{3} - 7 x^{2} + 14 x - 8)}{6} & \frac{x (x^{3} - 6 x^{2} + 11 x - 6)}{24} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \\ y_{3} \\ y_{4} \end{matrix}]

⋮

⋮

y = [\begin{matrix} \frac{x^{8} - 36 x^{7} + 546 x^{6} - 4536 x^{5} + 22449 x^{4} - 67284 x^{3} + 118124 x^{2} - 109584 x + 40320}{40320} & \frac{- x (x^{7} - 35 x^{6} + 511 x^{5} - 4025 x^{4} + 18424 x^{3} - 48860 x^{2} + 69264 x - 40320)}{5040} & \frac{x (x^{7} - 34 x^{6} + 478 x^{5} - 3580 x^{4} + 15289 x^{3} - 36706 x^{2} + 44712 x - 20160)}{1440} & \frac{- x (x^{7} - 33 x^{6} + 447 x^{5} - 3195 x^{4} + 12864 x^{3} - 28692 x^{2} + 32048 x - 13440)}{720} & \frac{x (x^{7} - 32 x^{6} + 418 x^{5} - 2864 x^{4} + 10993 x^{3} - 23312 x^{2} + 24876 x - 10080)}{576} & \frac{- x (x^{7} - 31 x^{6} + 391 x^{5} - 2581 x^{4} + 9544 x^{3} - 19564 x^{2} + 20304 x - 8064)}{720} & \frac{x (x^{7} - 30 x^{6} + 366 x^{5} - 2340 x^{4} + 8409 x^{3} - 16830 x^{2} + 17144 x - 6720)}{1440} & \frac{- x (x^{7} - 29 x^{6} + 343 x^{5} - 2135 x^{4} + 7504 x^{3} - 14756 x^{2} + 14832 x - 5760)}{5040} & \frac{x (x^{7} - 28 x^{6} + 322 x^{5} - 1960 x^{4} + 6769 x^{3} - 13132 x^{2} + 13068 x - 5040)}{40320} \end{matrix}] \cdot [\begin{matrix} y_{0} \\ y_{1} \\ y_{2} \\ y_{3} \\ y_{4} \\ y_{5} \\ y_{6} \\ y_{7} \\ y_{8} \end{matrix}]

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