How do you simplify #(x-3)^3#?

2 Answers
May 5, 2017

Answer:

#x^3-9x^2+27x-27#

Explanation:

#"Given " (x+a)(x+b)(x+c)" then expansion is"#

#x^3+(a+b+c)x^2+(ab+bc+ac)x+abc#

#rArr(x-3)^3#

#=(x-3)(x-3)(x-3)#

#"with " a=b=c=-3#

#rArr(x-3)^3#

#=x^3+(-3-3-3)x^2+(9+9+9)x#
#color(white)(xx)+(-3)(-3)-3)#

#=x^3-9x^2+27x-27#

Answer:

An alternate way to work it using binomial expansion

Explanation:

An alternate way to do this is to use Binomial Expansion, which uses the general formula of:

#(a+b)^n=(C_(n,0))a^nb^0+(C_(n,1))a^(n-1)b^1+...+(C_(n,n))a^0b^n#

So here we have:

  • #a=x#
  • #b=-3#
  • #n=3#

#((C,a,b,"term"),(1,x^3,1,x^3),(3,x^2,-3,-9x^2),(3,x,9,27x),(1,1,-27,-27))#

and we add them up:

#x^3-9x^2+27x-27#