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.

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

= $(x-3)(x(x-3)-3(x-3))$

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

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

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

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

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

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