How do you use the binomial series to expand #(2x^3 – 3)^10#?

1 Answer
sankarankalyanam
Jan 29, 2018

As explained below

Explanation:

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10th row of Pascal's triangle

1 10 45 120 210 252 210 120 45 10 1

#(2x^3 - 3)^10 = 1*(2x^3)^10 3^0 - 10 (2x^3)^9 3^1 + 45 (2x^3)^8 3^2 - 120 (2x^3)^7 3^3 + 210 (2x^3)^6 3^4 - 252 (2x^3)^5 3^5 + 210 (2x^3)^4 3^6 - 120 (2x^3)^3 3^7 + 45 (2x^3)^2 3^8 - 10 (2x^3)^1 3^9 + 1 (2x^3)^0 3^10#

#color(blue)((2x^3 - 3)^10= 2^10 x^30 - (30*2^9)x^27 + (405*2^8)x^24 - (3240 * 2^7)x^21 + (210 * 2^6 * 3^4) x^18 - (252 * 2^5 * 3^5) x^15 + (3360 * 3^6)x^12 - (960 * 3^7) x^9 + (180 * 3^8) x^6 - (20 * 3^9)x^3 + 3^10))#

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