This is an assignment question from the topic 'Interpolation' I tried to begin this sum by calculating $\Delta^4=y_4-4y_3+6y_2-4y_1+y_0$
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Start with \begin{align} (Δy)(x)&=y(x+1)-y(x) \\ &=(3x+4)(3x+7)···(3x+22)·\bigl((3x+25)-(3x+1)\bigr) \\ &=24·(3x+4)(3x+7)···(3x+22) \end{align}
Continue with $$ (Δy)(x+1)=24·(3x+7)(3x+10)···(3x+25) $$
Lutz Lehmann
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From where did (3x+25) come? And why (3x+1) is being subtracted from it? – Jignesh Shah Apr 02 '16 at 10:50
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$y(x+1)=(3x+4)···(3x+25)$ and extracting common factors from the difference $y(x+1)-y(x)$. – Lutz Lehmann Apr 02 '16 at 17:22