Question 36: Calculate the value of the expression \(B=x^{10}+20 x^{9}+20 x^{8}+\ldots+20 x^{2}+20 x+20 \text { with } x=-19 .\)
With x = – 19, so we substitute 20 = – x + 1 into the expression, we have:
\(\begin{aligned} &B=x^{10}+(-x+1) x^{9}+(-x+1) x^{8}+\ldots+(-x+1) x^{ 2}+(-x+1) x+(-x+1) \\ &B=x^{10}-x^{10}+x^{9}-x^{9}+x^{8}- x^{8}+\ldots+x^{2}-x^{2}+x-x+1 \\ &B=1 . \end{aligned}\)
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