binomial theoram

Do it systematically, for example,

(a+b)ⁿ = aⁿ + na^n-1b + n(n-1)a^n-2b²/(1.2) + n(n-1)(n-2)a^n-3b³/(1.2.3) +.................+ bⁿ 

Comparing (1-2x)⁵ we write, a = 1 and b = -2x.

(1-2x)⁵ = (1)⁵ - 5(1)^5-1(2x)¹ + 5x4(1)^5-2(-2x)²/(1.2) + 5(5-1)(5-2)(1)^5-3(-2x)³/(1.2.3) +

5(5-1)(5-2)(5-3)1^5-4(-2x)⁴/(1.2.3.4) + 5(5-1)(5-2)(5-3)(5-4)1^5-5(-2x)⁵/(1.2.3.4.5)

= 1 - 10x + 40x² - 80x³ + 80x⁴ - 32x⁵

Regards,

Team,

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