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2018年4月8日 · We can expand the expression using the binomial theorem: (x −1)4 ≡ 4 ∑ r=0(n r)(x)r(−1)n−r. = x4 − 4x3 + 6x2 −4x + 1. We could also you the appropriate row from Pascal's …

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Using Pascal's triangle gives \displaystyle{81}{x}^{{4}}-{108}{x}^{{3}}+{54}{x}^{{2}}-{12}{x}+{1} . Explanation: To expand \displaystyle{\left({3}{x} …

Use the binomial expansion theorem to find each term. The binomial theorem states (a + b)n = n ∑ k = 0nCk ⋅ (an - kbk). 4 ∑ k = 0 4! (4 - k)!k! ⋅ (1)4 - k ⋅ (- x)k. Expand the summation.

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2018年5月2日 · #(a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4# so here, #a=x and b=1# We get: #(x+1)^4 = x^4+4x^3(1)+6x^2(1)^2+4x(1)^3+(1)^4# #(x+1)^4 = x^4+4x^3+6x^2+4x+1#

2016年9月24日 · According to Binomial Theorem expansion of #(x+a)^n# is #x^n+nx^(n-1)a+(n(n-1))/(2!)x^(n-2)a^2+(n(n-1)(n-3))/(3!)x^(n-3)a^3+(n(n-1)(n-3)(n-4))/(4!)x^(n-4)a^4+.....+a^n# …