Can you expand (x-1)^4 ?

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Aug 26, 2017

Answer:

#x^4 - 4x^3+6x^2-4x+1#

Explanation:

We need to expand #(x-1)^4#. Using Pascal's triangle , we know that the coefficients of each progressive terms are: #1# #4# #6# #4# #1#.

We also know from the binomial theorem that when we perform an expansion of #(a+b)^n, n in ZZ^+#, the exponent of #a# in each term decreases from #n# to #0# and the exponent of #b# in each term increases from #0# to #n#.

In this expansion, #x# has a positive coefficient, so the sign will stay the same, but #-1# will have a sign change for every alternating term.

Bearing all of this in mind,

#(x-1)^4#
#=1(-1)^0x^4+4(-1)^1x^3+6(-1)^2x^2#
#+4(-1)^3x^1+1(-1)^4x^0#

#=x^4-4x^3+6x^2-4x+1#

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