What is the standard form of #y=(x - 3)^3 #?

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Answer 1 · 2016-06-30T05:56:13

In standard form #y=x^3-9x^2+27x-27#

In #y=(x-3)^3#, the RHS is a polynomial of degree #3# in #x#.

The standard form of a polynomial in degree #3# is #ax^3+bx^2+cx+d#, so we should expend #(x-3)^3# by multiplying.

#(x-3)^3=(x-3)(x-3)^2#

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

= #(x-3)(x^2-3x-3x+9)#

= #(x-3)(x^2-6x+9)#

= #x(x^2-6x+9)-3(x^2-6x+9)#

= #x^3-6x^2+9x-3x^2+18x-27#

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