Expansion of (x-1)^4?

1 Answer
Apr 8, 2018

Answer:

# (x-1)^4 -= x^4 -4 x^3 + 6x^2- 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.