How do you use the binomial series to expand (x - 10z)^7(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)^7x7−70x6z+2100x5z2−35000x4z3+350000x3z4−21⋅105x2z5+7⋅106xz6−(10z)7

Explanation:

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a = x, b = -10za=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−10z)7=x7−7x6(10z)+21x5(10z)2−35x4(10z)3+35x3(10z)4−21x2(10z)5+7x(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)^7x7−70x6z+2100x5z2−35000x4z3+350000x3z4−21⋅105x2z5+7⋅106xz6−(10z)7

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