Expansion of (x-1)^4?
1 Answer
Apr 8, 2018
(x-1)^4 -= x^4 -4 x^3 + 6x^2- 4x+1(x−1)4≡x4−4x3+6x2−4x+1
Explanation:
We can expand the expression using the binomial theorem:
(x-1)^4 -= sum_(r=0)^4 ( (n), (r) ) (x)^r(-1)^(n-r)
" " = ( (4), (0) ) (x)^4(-1)^0 + ( (4), (1) ) (x)^3(-1)^1 +
" " ( (4), (2) ) (x)^2(-1)^2 + ( (4), (3) ) (x)^1(-1)^3 +
" " ( (4), (4) ) (x)^0(-1)^4
" " = ( 1 ) (x^4)(1) + ( 4 ) (x^3)(-1) + ( 6 ) (x^2)(1) +
" " ( 4 ) (x)(-1) + ( 1 ) (1)(1)
" " = x^4 -4 x^3 + 6x^2- 4x+1
We could also you the appropriate row from Pascal's Triangle to gain the coefficients.
