How do you use the binomial series to expand #(x - 10z)^7#?

1 Answer
sankarankalyanam
Jan 28, 2018

#x^7 - 70x^6z + 2100x^5z^2 - 35000 x^4 z^3 + 350000x^3z^4 - 21 * 10^5 x^2z^5 + 7 * 10^6 x z^6 - (10z)^7#

Explanation:

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#a = x, b = -10z#

Terms will have coefficients

1 7 21 35 35 21 7 1 in that order.

#(x-10z)^7 = x^7 - 7 x^6 (10z) + 21 x^5 (10z)2 - 35 x^4 (10z)^3 + 35 x^3 (10z)^4 - 21 x^2 (10z)^5 + 7 x (10z)^6 - (10z)^7#

#x^7 - 70x^6z + 2100x^5z^2 - 35000 x^4 z^3 + 350000x^3z^4 - 21 * 10^5 x^2z^5 + 7 * 10^6 x z^6 - (10z)^7#

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